Lichess is a completely free, open-source platform sustained by donations. It lets you play against 8 levels of Stockfish (its AI) for free, with no ads or paywalls. The interface is clean and fast, appealing for blitz and bullet practice. Lichess also has built-in analysis tools: after any game you get a free engine evaluation of your moves, plus unlimited tactics puzzles and opening studies. In short, Lichess offers powerful training and AI play at no cost.
Visit Lichess.org (Web, iOS, Android)