A K Peters/CRC Press
This introductory textbook describes fundamental groups and their topological soul mates, the covering spaces. The author provides several illustrative examples that touch upon different areas of mathematics, but in keeping with the books introductory aim, they are all quite elementary. Basic concepts are clearly defined, proofs are complete, and no results from the exercises are assumed in the text.
" ""A welcome addition to the library of basic topology."" - J. McCleary, Vassar College -J. McCleary, Vassar College, CHOICE Magazine, March 2004
""In addition to the lucid writing… and plentiful exercises, another nice feature of Lima's book is a number of references to the history of the ideas which he is presenting."" -Darren Glass, MAA Online , March 2004
""This is a book that all libraries should have, not because it is encyclopedic, but because it introduces the student to a variety of accessible applications and insights too quickly skimmed over in standard texts."" -Iain Aitchison, Australian Mathematical Society , November 2005
""Here is an excellent self-contained introduction to fundamental groups and covering spaces. It assumes only a few basic notions from topology . . . Though the book has a definite textbook feel to it, it provides an absorbing read for anyone interested in an introduction to algebraic topology. The text is interspersed with over 70 illustrative examples and over 50 well-drawn explanatory pictures. Overall, the book is clearly written and has a good flow to it and succeeds admirably in the task it set itself."" -Philip Maynard, The Mathematical Gazette , July 2004"
Part I: Fundamental Groups 1. Homotopy 2. The Fundamental Group 3. Some Examples and Applications 4. Classical Matrix Groups 5. The Winding Number Part II: Covering Spaces 6. Covering Spaces 7. Covering Maps and Fundamental Groups 8. Oriented Double Covering