  In these lecture notes for a summer mini-course, we provide an exposition on
quantum groups and Hecke algebras, including (quasi) R-matrix, canonical basis,
and $q$-Schur duality. Then we formulate their counterparts in the setting of
$\imath$quantum groups arising from quantum symmetric pairs, including (quasi)
K-matrix, $\imath$-canonical basis, and $\imath$Schur duality. As an
application, the ($\imath$-)canonical bases are used to formulate
Kazhdan-Lusztig theories and character formulas in the BGG categories for Lie
(super)algebras of type A-D. Finally, geometric constructions for $q$-Schur and
$\imath$Schur dualities are provided.
