This book gives an introduction to quantum mechanics with the matrix method Heisenberg's matrix mechanics is described in detail The fundamental equations are derived by algebraic methods using matrix calculus Only a brief description of Schroedinger's wave mechanics is given (in most books exclusively treated) to show their equivalence to Heisenberg's matrix method In the first part the historical development of Quantum theory by Planck Bohr & Sommerfeld is sketched followed by the ideas & methods of Heisenberg Born & Jordan Then Pauli's spin & exclusion principles are treated Pauli's exclusion principle leads to the structure of atoms Finally Dirac's relativistic quantum mechanics is shortly presented Matrices & matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE & Mathematica