John Baez's Lie Theory Page
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Michael Weiss's notes hosted on John Baez's site work through Lie groups and Lie algebras with quantum mechanics as the motivating application, covering adjoint representations, unitary matrices, spinors, and the Dirac equation for physics-minded readers.
More resources on Lie Groups
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
nLab: Lie Group
Encyclopedia entry defining Lie groups from a category-theoretic and differential-geometric standpoint, with links to Lie algebras, smooth manifolds, and higher generalizations. Useful as a precise reference once the basic definitions are already familiar.
Geometric Anatomy of Theoretical Physics
Learn Lie groups and their geometric anatomy with Frederic Schuller's theoretical physics course. Dive into advanced math concepts now!
Lie Groups, Lie Algebras, and Representations
Springer graduate text developing matrix Lie groups, their Lie algebras, the exponential map, and representation theory, deliberately avoiding general manifold theory. Readers finish able to classify representations of SU(2), SU(3), and semisimple Lie algebras.
Lie Groups: An Introduction Through Linear Groups
Oxford textbook introducing Lie theory through concrete linear (matrix) groups before abstract manifolds, covering the exponential map, Lie algebras, and representations. Suited to readers with linear algebra and calculus who want a computational entry point.
nLab
Collaborative wiki for mathematics, physics and philosophy written from a category-theoretic viewpoint, with cross-linked entries on categories, functors, adjunctions, topos theory, higher category theory and homotopy theory. Readers can look up precise definitions, examples and references for advanced structural mathematics.