diff --git a/MathInterpreter/Core/Exceptions.cs b/MathInterpreter/Core/Exceptions.cs
index f6770ba..6ce7a78 100644
--- a/MathInterpreter/Core/Exceptions.cs
+++ b/MathInterpreter/Core/Exceptions.cs
@@ -2,4 +2,59 @@
 
 namespace MathInterpreter.Core;
 
-// TODO implement all exception classes
+public abstract class ExpressionException : Exception
+{
+    /// <summary>
+    /// Initializes <see cref="ExpressionException"/> with the specified error <paramref name="message"/> and the optional <paramref name="innerException"/>
+    /// </summary>
+    /// <param name="message">The error message</param>
+    /// <param name="innerException">The optional exception</param>
+    protected ExpressionException(string message, Exception? innerException = null)
+        : base(message, innerException) { }
+}
+
+public sealed class ExpressionFormatException : ExpressionException
+{
+    /// <summary>
+    /// Initializes <see cref="ExpressionFormatException"/> with the specified error <paramref name="message" /> and the optional <paramref name="innerException"/>
+    /// </summary>
+    /// <param name="message">The error message</param>
+    /// <param name="innerException">The innerException</param>
+    public ExpressionFormatException(string message, Exception? innerException = null)
+        : base(message, innerException) { }
+}
+
+public sealed class OperatorException : ExpressionException
+{
+    /// <summary>
+    /// Initializes <see cref="OperatorException"/> with the specified error <paramref name="message"/>
+    /// </summary>
+    /// <param name="message">The error message</param>
+    public OperatorException(string message) : base(message) { }
+}
+
+public sealed class NumberFormatException : ExpressionException
+{
+    /// <summary>
+    /// Initializes <see cref="NumberFormatException"/> with the <paramref name="expression"/> and the optional <paramref name="reason"/>
+    /// </summary>
+    /// <param name="expression">The expression</param>
+    /// <param name="reason">The optional reason</param>
+    public NumberFormatException(ReadOnlySpan<char> expression, string? reason = null)
+        : base(FormatMessage(expression, reason)) { }
+    
+    private static string FormatMessage(ReadOnlySpan<char> expression, string? reason = null)
+    {
+        reason = string.IsNullOrWhiteSpace(reason) ? string.Empty : $" ({reason})";
+        return $"Unable to read number from beginning of '{expression}'{reason}";
+    }
+}
+
+public sealed class NumberValueException : ExpressionException
+{
+    /// <summary>
+    /// Initializes <see cref="NumberValueException"/> with the specified error <paramref name="message"/>
+    /// </summary>
+    /// <param name="message">The error message</param>
+    public NumberValueException(string message) : base(message) { }
+}
\ No newline at end of file
diff --git a/MathInterpreter/Core/ExpressionScanner.cs b/MathInterpreter/Core/ExpressionScanner.cs
index 430f2dd..026e14f 100644
--- a/MathInterpreter/Core/ExpressionScanner.cs
+++ b/MathInterpreter/Core/ExpressionScanner.cs
@@ -15,8 +15,28 @@ public static class ExpressionScanner
     /// <exception cref="OperatorException">Thrown if none or an unknown operator is found</exception>
     public static ScanResult<Operator> ScanOperator(ReadOnlySpan<char> expression)
     {
-        // TODO
-        throw new NotImplementedException();
+        int index = 0;
+        
+        while (index < expression.Length && char.IsWhiteSpace(expression[index]))
+        {
+            index++;
+        }
+    
+        if (index >= expression.Length)
+        {
+            throw new OperatorException("Empty expression");
+        }
+    
+        char op = expression[index];
+
+        return op switch
+               {
+                   '+' => new ScanResult<Operator>(Operator.Plus, 1, expression[(index + 1)..]),
+                   '-' => new ScanResult<Operator>(Operator.Minus, 1, expression[(index + 1)..]),
+                   '*' => new ScanResult<Operator>(Operator.Multiply, 1, expression[(index + 1)..]),
+                   '/' => new ScanResult<Operator>(Operator.Divide, 1, expression[(index + 1)..]),
+                   _   => throw new OperatorException($"Unknown operator: {op}")
+               };
     }
 
     /// <summary>
@@ -28,8 +48,74 @@ public static class ExpressionScanner
     /// <exception cref="ExpressionFormatException">Thrown if a problem with the format of the number is found</exception>
     public static ScanResult<double> ScanOperand(ReadOnlySpan<char> expression)
     {
-        // TODO
-        throw new NotImplementedException();
+        int index = 0;
+        
+        while (index < expression.Length && char.IsWhiteSpace(expression[index]))
+        {
+            index++;
+        }
+
+        if (index >= expression.Length)
+        {
+            throw new ExpressionFormatException("Operand is missing");
+        }
+
+        if (expression[index] == '.')
+        {
+            throw new ExpressionFormatException("Unable to parse integral part of number");
+        }
+        
+        if (!(char.IsDigit(expression[index]) || 
+              (index < expression.Length - 1 && (expression[index] == '+' || expression[index] == '-') && char.IsDigit(expression[index + 1]))))
+        {
+            throw new ExpressionFormatException("Operand is missing");
+        }
+
+        try
+        {
+            var integralResult = ScanNumber(expression, true);
+            int integralValue = integralResult.Value;
+            bool isNegative = integralValue < 0;
+            
+            ReadOnlySpan<char> remaining = integralResult.RemainingExpression;
+            index = 0;
+            
+            while (index < remaining.Length && char.IsWhiteSpace(remaining[index]))
+            {
+                index++;
+            }
+            
+            if (index >= remaining.Length || remaining[index] != '.')
+            {
+                return new ScanResult<double>(integralValue, integralResult.Length, remaining);
+            }
+            
+            ReadOnlySpan<char> fractionalPart = remaining[(index + 1)..];
+            
+            try
+            {
+                var fractionalResult = ScanNumber(fractionalPart, false);
+                double fractionalValue = fractionalResult.Value / Math.Pow(10, fractionalResult.Length);
+                
+                double result = Math.Abs(integralValue) + fractionalValue;
+                if (isNegative)
+                {
+                    result = -result;
+                }
+
+                return new ScanResult<double>(result,
+                    integralResult.Length + 1 + fractionalResult.Length,
+                    fractionalResult.RemainingExpression);
+            }
+            catch (NumberFormatException)
+            {
+                throw new ExpressionFormatException("Unable to parse fractional part of number");
+            }
+        }
+        catch (NumberFormatException)
+        {
+            throw new ExpressionFormatException("Unable to parse integral part of number");
+        }
     }
 
     /// <summary>
@@ -41,7 +127,70 @@ public static class ExpressionScanner
     /// <exception cref="NumberFormatException">Thrown if no or an invalid number is found</exception>
     public static ScanResult<int> ScanNumber(ReadOnlySpan<char> expression, bool allowSign)
     {
-        // TODO
-        throw new NotImplementedException();
+        int index = 0;
+        int sign = 1;
+        
+        while (index < expression.Length && char.IsWhiteSpace(expression[index]))
+        {
+            index++;
+        }
+        
+        if (index < expression.Length)
+        {
+            if (expression[index] == '+' || expression[index] == '-')
+            {
+                if (!allowSign)
+                {
+                    throw new NumberFormatException(expression, "Sign is not allowed here");
+                }
+                
+                if (expression[index] == '-')
+                {
+                    sign = -1;
+                }
+                index++;
+                
+                while (index < expression.Length && char.IsWhiteSpace(expression[index]))
+                {
+                    index++;
+                }
+                
+                if (index < expression.Length && (expression[index] == '+' || expression[index] == '-'))
+                {
+                    throw new NumberFormatException(expression, "Sign may occur only once");
+                }
+            }
+        }
+        
+        int value = 0;
+        int digitCount = 0;
+
+        while (index < expression.Length)
+        {
+            char c = expression[index];
+
+            if (char.IsDigit(c))
+            {
+                int digit = (int)char.GetNumericValue(c);
+                value = value * 10 + digit;
+                index++;
+                digitCount++;
+            }
+            else if (char.IsWhiteSpace(c))
+            {
+                index++;
+            }
+            else
+            {
+                break;
+            }
+        }
+        
+        if (digitCount == 0)
+        {
+            throw new NumberFormatException(expression);
+        }
+
+        return new ScanResult<int>(value * sign, digitCount, expression[index..]);
     }
 }
diff --git a/MathInterpreter/Core/MathExpression.cs b/MathInterpreter/Core/MathExpression.cs
index 388c4e5..3392223 100644
--- a/MathInterpreter/Core/MathExpression.cs
+++ b/MathInterpreter/Core/MathExpression.cs
@@ -8,13 +8,10 @@ namespace MathInterpreter.Core;
 /// </summary>
 public sealed class MathExpression
 {
-    // TODO
-    /*
     private double? _leftOperand;
     private Operator? _operator;
     private double? _result;
     private double? _rightOperand;
-    */
 
     /// <summary>
     ///     Creates a new instance of <see cref="MathExpression" /> from the provided expression string.
@@ -39,8 +36,29 @@ public sealed class MathExpression
     {
         get
         {
-            // TODO
-            throw new NotImplementedException();
+            if (_result.HasValue)
+            {
+                return _result.Value;
+            }
+
+            if (!_leftOperand.HasValue || !_operator.HasValue || !_rightOperand.HasValue)
+            {
+                throw new UnreachableException("Expression is not fully parsed");
+            }
+
+            double left = _leftOperand.Value;
+            double right = _rightOperand.Value;
+
+            _result = _operator.Value switch
+                      {
+                          Operator.Plus     => left + right,
+                          Operator.Minus    => left - right,
+                          Operator.Multiply => left * right,
+                          Operator.Divide   => left / right,
+                          _                 => throw new UnreachableException("Unknown operator")
+                      };
+
+            return _result.Value;
         }
     }
 
@@ -55,13 +73,69 @@ public sealed class MathExpression
     /// </exception>
     public override string ToString()
     {
-        // TODO
-        throw new NotImplementedException();
+        if (!_leftOperand.HasValue || !_operator.HasValue || !_rightOperand.HasValue)
+        {
+            throw new UnreachableException("Expression is not fully parsed");
+        }
+
+        string operatorSymbol = _operator.Value switch
+                                {
+                                    Operator.Plus     => "+",
+                                    Operator.Minus    => "-",
+                                    Operator.Multiply => "*",
+                                    Operator.Divide   => "/",
+                                    _                 => throw new UnreachableException("Unknown operator")
+                                };
+
+        return $"{_leftOperand.Value} {operatorSymbol} {_rightOperand.Value}";
     }
 
     private void ValidateAndParse(ReadOnlySpan<char> expression)
     {
-        // TODO
-        throw new NotImplementedException();
+        int index = 0;
+        while (index < expression.Length && char.IsWhiteSpace(expression[index]))
+        {
+            index++;
+        }
+
+        if (index < expression.Length)
+        {
+            char firstChar = expression[index];
+            if (firstChar is '+' or '*' or '/')
+            {
+                throw new OperatorException("Operator is missing");
+            }
+        }
+
+        try
+        {
+            var leftOperandResult = ExpressionScanner.ScanOperand(expression);
+            var operatorResult = ExpressionScanner.ScanOperator(leftOperandResult.RemainingExpression);
+            _leftOperand = leftOperandResult.Value;
+            _operator = operatorResult.Value;
+
+            try
+            {
+                var rightOperandResult = ExpressionScanner.ScanOperand(operatorResult.RemainingExpression);
+                _rightOperand = rightOperandResult.Value;
+
+                if (_operator == Operator.Divide && _rightOperand == 0)
+                {
+                    throw new NumberValueException("Division by zero is not allowed");
+                }
+            }
+            catch (ExpressionFormatException)
+            {
+                throw new ExpressionFormatException("Right operand is missing");
+            }
+        }
+        catch (ExpressionException)
+        {
+            throw;
+        }
+        catch (Exception ex)
+        {
+            throw new ExpressionFormatException("Unable to parse expression", ex);
+        }
     }
 }
diff --git a/MathInterpreter/Core/ScanResult.cs b/MathInterpreter/Core/ScanResult.cs
index 6d9f645..dca8db9 100644
--- a/MathInterpreter/Core/ScanResult.cs
+++ b/MathInterpreter/Core/ScanResult.cs
@@ -18,8 +18,13 @@ public readonly ref struct ScanResult<T> where T : struct
     /// <exception cref="ArgumentOutOfRangeException">Thrown if an invalid argument is provided</exception>
     public ScanResult(T value, int length, ReadOnlySpan<char> remainingExpression)
     {
+        if (length < 0)
+        {
+            throw new ArgumentOutOfRangeException(nameof(length), "Length must be non-negative");
+        }
+    
         Value = value;
-        Length = -1; // TODO
+        Length = length;
         RemainingExpression = remainingExpression;
     }