My favorites list.

MathSE chatroom co-owner alongside robjohn.

My answers with expository content (may update later):

• "Make-believe" free constructions in algebra
• Sets of lecture notes and articles
• Applications, motivations of the tensor product
• On tensoring with torsion, divisibility and fractions
• Terse description of local fields as $\bullet$-adic complections
• Cycle decomposition & orders of permutations as lcms
• Relation between ${\bf F}_p$ and ${\bf Z}_p$ via Witt vectors
• Cyclotomic structure of the $p$-adics ${\bf Q}_p$
• Representation theory generalizes 1D characters
• $S_n$ is complete for $n\ne2,6$
• Abelian implies Frattini = prime subgroups
• Ford circles, hyperbolic geometry & wt. $0$ modular forms
• Motivation, explanation of asymptotic notation
• Permutation centralizers via internal wreath products
• Characters of symmetric and exterior powers
• What's interesting about the zeros of $\zeta(s)$