σ cond (R)	Selection — keep tuples where cond is true; compose multiple σ to AND conditions
π a, b (R)	Projection — keep listed attributes; removes duplicate tuples (set semantics)
ρ S (R)	Rename — rename relation to S; use ρ S(a,b,…) (R) to also rename attributes
R ⋈ S	Natural Join — equi-join on all common attribute names; removes duplicate columns
R ⋈ (θ) S	Theta Join — join with explicit condition, e.g. `R ⋈ (R.id = S.fk) S`
𝔉 g, f(a)→n (R)	Aggregation — group by g; compute f(a) renamed to n; omit g for whole-table aggregate
R ∪ S	Union — all tuples in R or S; schemas must be union-compatible (same arity)
R ∩ S	Intersection — tuples in both R and S (union-compatible)
R − S	Difference — tuples in R not in S (union-compatible)
R × S	Cartesian Product — all pairs of tuples; use σ to filter (becomes theta join)
R ÷ S	Division — tuples of R whose R-S part is paired with every tuple of S

COUNT(*)	Count all tuples in the group
COUNT(a)	Count non-null values of attribute a
SUM(a)	Sum values of a across the group
AVG(a)	Arithmetic mean of a across the group
MIN(a)	Minimum value of a in the group
MAX(a)	Maximum value of a in the group

Expression

Expression Tree (click a node to inspect)