This book is dedicated to the study of algebraic characteristics of some structures of matroid type. The notions of pseudo-matroids generated by mappings of matroids, G-mappings of binary matroids and semi-matroids are introduced. Some results on general matroid theory and an algorithmic solution for exponential complexity of problems with enumeration of all non-isomorphic binary matroids are found. The theoretical results are applied to the solution of some practical problems. This monograph is beneficial to specialists in discrete mathematics and matroids, information transmission technologies, as well as students and post-graduates.