A study of Fibonacci sequences and the well-known Fibonacci numbers. It should be of interest to research mathematicians wishing to advance the ideas themselves, and to recreational mathematicians, who should enjoy the various visual approaches and the problems inherent in them. There is a continuing emphasis on diagrams, both geometric and combinatorial, which helps to tie disparate topics together, weaving around the unifying themes of the golden mean and various generalizations of the Fibonacci recurrence relation. Very little prior mathematical knowledge is assumed, other than the rudiments of algebra and geometry, so the text may be used as a source of enrichment material and project work for college students. A chapter on games using goldpoint tiles is included at the end, and it seeks to provide much material for stimulating mathematical activities involving geometric puzzles of a combinatoric nature.