Introduction. 1. Universal Sequences of Functors. 2. Derived Functors. 3. Extensions and Cohomology of Monoids with Coefficients in Semimodules. 4. Cohomology of Algebraic Theories and MacLane (co)Homology of Rings. 5. K-Functors. 6. Non-Abelian Homology and Cohomology of Groups. References.