This text deals with algebraic topology, homotopy theory and simple homotopy theory of infinite CW-complexes with ends. The homotopy theory is approached without the rather sophisticated notion of pro-category. Spaces spherical objects of CW-complexes in the category of spaces with ends, and all arguments refer directly to this category. In this way, infinite homotopy theory is presented as a natural extension of classical homotopy theory. In particular, this book introduces the construction of the proper groupoid of a space with ends and then the cohomology with local coefficients is defined by the enveloping ringoid of the proper fundamental groupoid. This volume should be of interest to researchers whose work involves algebraic topology, category theory, homological algebra, general topology, manifolds, and cell complexes.