LL(1) parsing
The name LL is two letters with a precise meaning: the first L says the parser reads the input Left to right, the second L says it builds a Leftmost derivation. The number in parentheses, the 1 in LL(1), says how many tokens of look-ahead it uses to decide what to do, here just one. So LL(1) parsing is: scan left to right, expand the leftmost nonterminal, and never need more than one token of peeking to choose a rule.
A grammar is LL(1) when one look-ahead token is always enough to pick the right production without ambiguity, which is exactly the condition that makes the predictive parsing table conflict-free. Formally, for any nonterminal with alternatives A -> alpha | beta, the FIRST sets of alpha and beta must be disjoint (no token could start both), and if one alternative can derive the empty string, its FOLLOW set must not clash with the other's FIRST set. When these conditions hold, you can build a recursive-descent or table-driven parser that runs in linear time with no backtracking. LL(1) is the simplest, most teachable parsing class, and LL(k) for larger k just allows peeking further ahead.
LL(1) parsing is popular because it is easy to understand, easy to hand-write, and gives friendly, localized error messages, which is why ANTLR-style tools and most textbook parsers lean on it. Its weakness is reach: LL grammars are a strict subset of what bottom-up LR parsers handle, and arithmetic written the natural left-recursive way (E -> E + T) is not LL at all and must be rewritten first. So LL trades some power for simplicity and clarity.
E -> T E', E' -> + T E' | epsilon, T -> num is an LL(1) grammar for sums: it is the left-recursion-free rewrite of E -> E + T | T. With E' you decide by one look-ahead: see a '+' and pick + T E', see end-of-input and pick epsilon.
LL(1): read Left-to-right, Leftmost derivation, 1 token of look-ahead, no backtracking.
LL parsers are strictly weaker than LR parsers: every LL(1) grammar is LR(1) but not the reverse. A grammar being un-LL does not mean its language is un-parseable, only that the natural top-down approach needs the grammar rewritten or a stronger method.