The goal of this book is to study some categorial aspects of the theory of topological abelian groups and topological modules. In topological algebra there is a small number of papers on categorial aspects of this theory. A problem which attracts the researchers’ attention is the epimorphisms characterization in the topological Hausdorff groups category. An important role in the categorial theory is played by the reflective subcategory concept. The famous Theorem of Birkhoff characterized varieties of algebraic systems as closed classes with respect to cartesian products, subalgebras and homomorphic images. There are more variety concepts for topologico-algebraic systems. A strong construction in topological algebra is the tensor products of modules and abelian groups. This monograph is addressed to researchers and graduate students for research, seminars and advanced graduate courses in topological algebra.