Syllabus (Tentative) General introduction. Matchings. Flows. LPs. Duality. Polyhedral characterizations of matchings. Basic graph theory around matching. Unweighted bipartite matching. Hofcroft-Karp. Hungarian algorithm for assignment problem. Scaling for faster assignment problem. Gabow-Tarjan Auction algorithm for matching. Parallel matching Karp Upfal Wigderson , Mulmuley, Vazirani and Vazirani Sublinear time algorithms for parallel matching. Goldberg Plotkin Vaidya. Interior point algorithms -- Goldberg, Plotkin, Shmoys, Tardos Maximal matchings using map-reduce Non-bipartite matching. Micali-Vazirani, Vazirani. Matchings and game theory. Stable Marriages. Average-case algorithms for matching. Motwani Clique partitions and accelerating matching. Motwani Feder Online b-matching . Kanasundaram Pruhs Adwords problem. Metha et. al. Online primal-dual for adwords. Buchbinder Jain. Stochastic adwords problem. Feldman et. al. Getting both a stochastic and a determistic guarantee. Miirokni et. al. Learning in matching. Henzinger et. al. Online stochastic matching Other recent online matching results. Stable marriages. Applications of matchings Other topics.