This is a series of research projects that can be used for enrichment of the high school mathematics curriculum. It is suggested that the topics are either not found in the standard curriculum or represent a more indepth study of standard topics. The areas considered are: applications of the microcomputer in mathematics; the fourth dimension and beyond; finite groups; transfinite numbers; Pythagoras and his theorem; topology; geometric inversion; the mathematics of flight; paradoxes in mathematics; continued fractions; finding equations from tables of values; tessellations; transformations and matrices with applications; statistics; pi and its history; and Pascal and his triangle. A guide following many projects furnishes essential information or hints and some include drawings to present crucial information. The references are listed near the end of each unit. Many of the units include ideas for further investigation. The material has been put into reproducible form for student use. The teacher notes for each unit include key information and solutions when appropriate. (PK)