P
Also known as: Polynomial Time, Deterministic Polynomial Time
P is the class of decision problems solvable by a deterministic Turing machine in polynomial time: time $O(n^k)$ for some fixed $k$ in the input size $n$.
Sorting-related decisions, shortest paths in graphs with nonnegative weights, and 2-SAT sit in P. These are the problems theory treats as “tractable” in the worst-case asymptotic sense.
P $\subseteq$ NP. Whether equality holds is open. NP-complete problems are the candidates that would collapse the two classes if any one of them fell into P.