Generalized notions of continued fractions : ergodicity and number theoretic applications There is no clear sense of when the continued fraction was originally conceived of. It is likely that one of the first authors who indirectly suggested this notion was Euclid (c. 300 BC) via his famous algorithm (the oldest nontrivial algorithm that has survived to the present day) in the seventh book of his Elements. Since then Aryabhata Fibonacci Bombelli Wallis Huygens and Euler have developed this theory and it continues to evolve today especially as a means of linking different areas of mathematics. This book whose primary audience is graduate students and senior researchers is motivated by the fascinating interrelations between ergodic theory and number theory (as established since the 1950s). It examines several generalizations and extensions of classical continued fractions including generalized Lehner simple and Hirzebruch Jung continued fractions