How should you encode a message to an extraterrestrial? What do frogs and powers of 2 have in common? How many faces does the Stella Octangula have? Is a plane figure of constant diameter a circle, and what has this to do with NASA? 210 = 5 x 6 x 7 = 14 x 15, so just how many numbers can be the product of both two and of three consecutive integers? Is there any such thing as a truly correct map? What patterns are possible in juggling?What do all of these questions have in common? They, and many others, are answered in this book.The authors are distinguished mathematicians; some are bright newcomers while others have been well known in mathematical circles for decades.This is a partial record of the Bay Area Math Adventures (BAMA), a lecture series for high school students (and incidentally their teachers, parents, and other interested adults) hosted by San Jose State and Santa Clara Universities in the San Francisco Bay Area. These lectures are aimed primarily at bright high school students, the emphasis on bright, and as a result, the mathematics in some cases is far from what one would expect to see in talks at this level. There areserious mathematical issues addressed here.We hope that this book will capture some of the magic of these talks that have filled auditoriums at the host schools almost monthly for several years. Join the students in sharing these mathematical adventures.