In the educational manual the fundamentals of quantum theory of angular momentum are given, a problem for eigen functions and eigen values of angular momentum operator is formulated, quantization and matrix elements of the momentum operator, vector coupling of two, three and more momenta are given, construction of spin and orbital wave functions of particles, spin quantum theory, problems and examples are detailed. This manual is assigned for students, master students and PhD students attended a general course of quantum mechanics in a volume being given to students of the department of physics. The knowledge of nuclear physics in a volume of a course of general physics is assumed.