Elementary properties of monoids, acts and categories: sets and relations; groupoids, semigroups and monoids; some classes of semigroups; acts over monoids (monoid automata); decompositions and components; categories; functors. Constructions: products and coproducts; pullbacks and pushouts; free objects and generators; cofree objects and generators; tensor products; wreath products of monoids and acts; the wreath product of a monoid with a small category. Classes of acts: injective acts; divisible acts; principally weakly injective acts; fg-weakly injective acts; absolutely pure acts; cogenerators and overview; torsion free acts; flatness of acts and related properties; principally weakly flat acts; weakly flat acts; flat acts; acts satisfying condition (P); acts satisfying condition (E); equalizer flat acts; pullback flat acts and overview; projective acts; generators; regular acts and overview. Homological classification of monoids: principal weak injectivity; on fg-weak injectivity; weak injectivity; absolute purity; injectivity and overview; torsion freeness and principal weak flatness; flatness; condition (P); strong flatness; projectivity; projective generators; freeness and overview; regularity of acts. Equivalence and duality: adjoint functors; categories equivalent to act - S Morita equivalence of monoids; endomorphism monoids of generators; on morita duality.
