\chapcontents {1}{Introduction}{3} \seccontents {1.1}{Short math background} {3} \seccontents {1.2}{Installation instructions} {5} \seccontents {1.3}{Quick example} {6} \chapcontents {2}{Properties and operations with groups and semigroups}{10} \seccontents {2.1}{Creation of groups and semigroups} {10} \seccontents {2.2}{Basic properties of groups and semigroups} {13} \seccontents {2.3}{Operations with groups and semigroups} {17} \seccontents {2.4}{Self-similar groups and semigroups defined by the wreath recursion} {24} \seccontents {2.5}{Contracting groups} {27} \seccontents {2.6}{Rewriting Systems} {29} \chapcontents {3}{Properties and operations with group and semigroup elements}{31} \seccontents {3.1}{Creation of tree automorphisms and homomorphisms} {31} \seccontents {3.2}{Properties and attributes of tree automorphisms and homomorphisms} {32} \seccontents {3.3}{Operations with tree automorphisms and homomorphisms} {34} \seccontents {3.4}{Elements of groups and semigroups defined by wreath recursion} {36} \seccontents {3.5}{Elements of contracting groups} {37} \chapcontents {4}{Noninitial automata}{38} \seccontents {4.1}{Definition} {38} \seccontents {4.2}{Tools} {39} \chapcontents {5}{Miscellaneous}{44} \seccontents {5.1}{Converters to and from FR package} {44} \seccontents {5.2}{Trees} {46} \seccontents {5.3}{Some predefined groups} {46} \chapcontents {}{Index}{50} \chapcontents {}{Bibliography}{53}