Glimpses of Algebra and Geometry is intended for a "Bridge Course" that facilitates the transition between undergraduate and graduate studies. This new edition includes innumerable improvements throughout the text, including an in-depth treatment of root formulas, a detailed and complete classification of finite Mobius groups a la Klein, and a quick, direct, and modern approach to Felix Klein's "Normalformsatz."

"A Number Is a Multitude Composed of Units"-Euclid.- "... There Are No Irrational Numbers at All"-Kronecker.- Rationality, Elliptic Curves, and Fermat's Last Theorem.- Algebraic or Transcendental?.- Complex Arithmetic.- Quadratic, Cubic, and Quartic Equations.- Stereographic Projection.- Proof of the Fundamental Theorem of Algebra.- Symmetries of Regular Polygons.- Discrete Subgroups of Iso (R2).- Möbius Geometry.- Complex Linear Fractional Transformations.- "Out of Nothing I Have Created a New Universe"-Bolyai.- Fuchsian Groups.- Riemann Surfaces.- General Surfaces.- The Five Platonic Solids.- Finite Möbius Groups.- Detour in Topology: Euler-Poincaré Characteristic.- Detour in Graph Theory: Euler, Hamilton, and the Four Color Theorem.- Dimension Leap.- Quaternions.- Back to R3!.- Invariants.- The Icosahedron and the Unsolvable Quintic.- The Fourth Dimension.