Chapter 1, entitled "Basic topology", contains some selected basic results on the topology of separable metrizable spaces: linear spaces, the Michael Selection Theorem, basic ANR-theory, topological characterizations of some familiar spaces (Cantor set, the spaces of rationals and irrationals, the closed interval), inductive constructions of homeomorphisms (with applications to the topological homogeneity of the Hilbert cube and countable dense homogeneous spaces), near homeomorphisms and Bing's shrinking criterion, homogeneous zero-dimensional spaces, the Hurewicz Theorem and characterization of hereditarily Baire spaces, inverse limits (with application to indecomposable continua), hyperspaces.

Chapter 2, entitled "Basic combinatorial topology", contains basic information on simplices and simplicial complexes, and nerves of open covers. Among the main results of this chapter are Freudenthal's Approximation Theorem (on approximation of compacta by polyhedra) and Brouwer's Fixed-Point Theorem proved with the help of Sperner's Lemma.

Chapter 3, entitled "Basic dimension theory", contains, besides the standard core of the dimension theory of separable metrizable spaces, some interesting recent results, not covered in standard textbooks on dimension theory. These concern almost zero-dimensional spaces, higher-dimensional hereditarily indecomposable continua, Henderson compacta, weakly $n$-dimensional spaces, the colorings of maps, and the study of relationships between the standard dimension functions and the earlier Dimensionsgrad of Brouwer.

In Chapter 4, entitled "Basic ANR theory", the author generalizes the classical theory of ANRs to so-called ANR-pairs. An ANR-pair is a pair $(X,Y)$ consisting of a usual ANR $X$ and a homotopy dense subspace $Y\subset X$. The latter means that there is a homotopy $h\colon X\times[0,1]\to X$ with $h(x,0)=x$ and $h(x,t)\in Y$ for all $x\in X$ and $t\in(0,1]$. This chapter also includes the Curtis-Schori-West Theorem on the topological equivalence of the hyperspace of a Peano continuum and the Hilbert cube.

Chapter 5, entitled "Basic infinite-dimensional topology", introduces some infinite-dimensional techniques, in particular, $Z$-sets, (estimated) extension homeomorphisms between $Z$-sets in the Hilbert cube $Q$ or its pseudo-interior $s$, capsets in $Q$ and some of its hyperspace realizations. Next, the technique of absorbing systems is described and an application to identifying the topology of the hyperspace of infinite-dimensional compacta in $Q$ is presented.

Finally, Chapter 6, entitled "Function spaces", describes some recent results in $C\sb p$-theory, in particular, the description of the Borel complexity of $C\sb p$-spaces, the characterization of Baire spaces $C\sb p(X)$ (in particular, Baire $C\sb p$-spaces over countable spaces with a unique non-isolated point), the preservation of compactness, dimension, and topological completeness by $ l$-equivalence, the preservation of scattered spaces with finite scattered height by $ l\sp *$-equivalence, and the preservation of countable dimensionality by $t$-equivalence. The culminating result of the sixth chapter is the Dobrowolski-Marciszewski-Mogilski Theorem asserting that for a regular countable non-discrete space $X$ the function space $C\sb p(X)$ is homeomorphic to the countable power of the pseudo-boundary of the Hilbert cube if and only if $C\sb p(X)$ is an absolute $F\sb {\sigma\delta}$-set. The sixth chapter ends with a section consisting of 20 examples of crucial importance for $C\sb p$-theory.

The book ends with three appendices. Appendix A collects together some elementary topological facts discussed in the book. Each section of the book is completed by carefully selected exercises, and Appendix B contains answers to the most important exercises. Appendix C contains historical notes and comments.

We strongly recommend this book to mathematicians working in $C\sb p$-theory, infinite-dimensional topology, or dimension theory and also to students interested in these topics.