Revision history

• 2024-04-20 (changed equals to isomorphic in one equation, added a note about Bott periodicity)
• 2024-04-16 (added another definition of semisimple for compact connected Lie groups, added a footnote defining semisimple for not-necessarily-compact Lie groups, added a section with examples for a general structure theorem, added a section about maximal tori and rank, added a sentence relating the rank to the notation, added sections about homology groups and torsion, added a section about cohomology rings and their relationship to homology groups, changed "group" to "compact topological group" in the footnote about Tannaka-Krein duality and removed an unhelpful reference)
• 2024-04-08 (first version)