\chapcontents {1}{Introduction}{3} \seccontents {1.1}{Short math background} {3} \seccontents {1.2}{Installation instructions} {5} \seccontents {1.3}{Quick example} {5} \chapcontents {2}{Properties and operations with groups and semigroups}{9} \seccontents {2.1}{Creation of groups and semigroups} {9} \seccontents {2.2}{Basic properties of groups and semigroups} {12} \seccontents {2.3}{Operations with groups and semigroups} {16} \seccontents {2.4}{Self-similar groups and semigroups defined by wreath recursion} {23} \seccontents {2.5}{Contracting groups} {25} \seccontents {2.6}{Rewriting Systems} {27} \chapcontents {3}{Properties and operations with group and semigroup elements}{29} \seccontents {3.1}{Creation of tree automorphisms and homomorphisms} {29} \seccontents {3.2}{Properties and attributes of tree automorphisms and homomorphisms} {30} \seccontents {3.3}{Operations with tree automorphisms and homomorphisms} {32} \seccontents {3.4}{Elements of groups and semigroups defined by wreath recursion} {34} \seccontents {3.5}{Elements of contracting groups} {34} \chapcontents {4}{Noninitial automata}{36} \seccontents {4.1}{Definition} {36} \seccontents {4.2}{Tools} {37} \chapcontents {5}{Miscellaneous}{40} \seccontents {5.1}{Trees} {40} \seccontents {5.2}{Some predefined groups} {40} \chapcontents {}{Index}{44} \chapcontents {}{Bibliography}{47}