The aim of this project is to develop and implement algorithms for the construction of complete lists of pairwise non-isomorphic structures with certain properties. These structures can be graphs, maps, or even (models of) molecules. Such lists are used, for example, to test conjectures, to prove theorems (if they are reduced to a finite number of structures), to find examples, or simply to have an insight into the behavior of certain invariants. Some specific aims of the project are: to find graphs with few Hamiltonian cycles, to prove the minimality of a graph without a spanning 2-tree, and to develop a program for enumerating maps on orientable surfaces and to develop a program for enumerating planar polycyclic hydrocarbons with a given formula (this is already being worked on).