Twenty years of graduate-level seminars have been turned into a free online textbook. Both the 1985 edition and the 2012 update are available as PDF files.
Free Geometry Textbooks
Of all of the math courses that I have taken, I suspect things I learned in geometry class have been the most useful. Measuring circles, squares, and angles are useful in quilting, crafting, building and even cooking. Those basic skills in geometry have come in handy more than once. Students often find the subject challenging and hopefully, these free online geometry textbooks will offer some help.
Geometry is generally divided into four areas – Euclidean geometry, differential geometry, topology and geometry and algebraic geometry.
Euclidean geometry is used in the study of computational geometry, computer graphics, convex geometry, discrete geometry, some areas of cominatorics and crystallography. Euclidean geometry is what most of us study in high school.
Differential geometry has become more important in the field of mathematical physics due to Einstein’s general relativity postulation that the universe is curved. Wikipedia describes contemporary differential geometry as intrinsic, meaning that the spaces it considers are smooth manifolds whose geometric structure is governed by a Riemannian metric, which determines how distances are measured near each point, and not a priori parts of some ambient flat Euclidean space.
Topology and geometry is in a technical sense a type of transformation geometry where transformations are homeomorphisms. While geometric topography, differential topology and Morse theory are considered part of the field of geometry, algebraic topography and general topology are not.
Algebraic Geometry combines techniques of abstract algebra, especially commutative algebra, with the language and problems of geometry. It is used in complex analysis, topology and number theory.
Hopefully, students will find one of these free online geometry textbooks helpful in their own academic endeavors.