This is a nice book on descriptive set theory. While keeping the technical prerequisites to a minimum, it contains rich materials of the theory, especially its recursive aspects, from the very obvious ones to the research frontier, such as Borel sets, hyperarithmetic sets, perfect sets, the axiom of determinacy, the axiomatic system KP, the better quasiordering etc. The authors have their own ideas concerning descriptive set theory and mathematics in general as follows. The primary concern of mathematical logic is to explore the nature of infinity so as to clarify and explain its mathematical applications. The discovery of the higher infinities, e.g. uncountable cardinals etc., and their relevance to the lower infinities of analysis gave rise to descriptive set theory. Some natural mathematical statements need various strong assumptions in their proofs, and this fact is very important in current works. Anyone being interested in such subject might get ideas and motivations from this book.