The first edition of this book was published in 1968. In the preface to the first edition, Carl Boyer mentions some other books about the history of mathematics and why he thinks it is necessary to write just another one. The most important reason for him is strict adherence to chronological arrangement and a stronger emphasis on historical elements. From my point of view, this aim is (at once) the strength and the weakness of the book. In this single volume of more than 700 pages, the book supplies you with so much detailed historical facts and numbers that it really deserves to be called "A History Of Mathematics". But soon after starting to read the book, I lost interest in reading it. Why was it so boring to read facts and even more facts ? The wealth of material alone does not answer the questions about the history of mathematical ideas.
But Boyer also supplied the solution to this problem. Among the books he recommends in the preface of the first edition is a much shorter book by Howard Eves (Foundations and Fundamental Concepts Of Mathematics, ISBN 0-486-69609-X). Eves' book emphasizes the historical development of the most important ideas and methods through more than 2000 years. After reading Eves' book, you can return to Boyer's book and you will appreciate the wealth of details much more because your mind is equipped with a guideline.
There is one other fact worth mentioning about the book. The avaiable second edition has been revised by Uta C. Merzbach and Isaac Asimov has written a foreword. Merzbach left the first 22 chapter virtually unchanged. The chapters about more recent developments have been expanded. In revising the references and the bibliography, Merzbach replaced Boyer's references (often non-English sources) by works in English. That is good for the English-speaking readers, but is it also good for people who are interested in the history of mathematics (which mostly took place in Europe: Greece, Italy, France, Germany) ? The second major change Merzbach made was dropping the exercises. For a history book, this was probably the right decision. But in Eves' book (focused on the development of ideas), the exercises are a valuable means of deepening the understanding of the era and its problems.
To whom can I recommend this book ? I recommend this book to the initiated readers. If you have never heard about the axiomatic method, you should probably first read Eves' book and then return to this one.