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Transactional memory (TM) has shown potential to simplify the task of writing concurrent programs. TM shifts the burden of managing concurrency from the programmer to the TM algorithm. The correctness of TM algorithms is generally proved manually. The goal of this thesis is to provide the mathematical and software tools to automatically verify TM algorithms under realistic memory models. Our first contribution is to develop a mathematical framework to capture the behavior of TM algorithms and the required correctness properties. We consider the safety property of opacity and the liveness properties of obstruction freedom and livelock freedom. We build a specification language of opacity. We build a framework to express hardware relaxed memory models. We develop a new high-level language, Relaxed Memory Language (RML), for expressing concurrent algorithms with a hardware-level atomicity of instructions, whose semantics is parametrized by various relaxed memory models. We express TM algorithms like TL2, DSTM, and McRT STM in our framework. The verification of TM algorithms is difficult because of the unbounded number, length, and delay of concurrent transactions and the unbounded size of the memory. The second contribution of the thesis is to identify structural properties of TM algorithms which allow us to reduce the unbounded verification problem to a language-inclusion check between two finite state systems. We show that common TM algorithms satisfy these structural properties. The third contribution of the thesis is our tool FOIL for model checking TM algorithms. FOIL takes as input the RML description of a TM algorithm and the description of a memory model. FOIL uses the operational semantics of RML to compute the language of the TM algorithm for two threads and two variables. FOIL then checks whether the language of the TM algorithm is included in the specification language of opacity. FOIL automatically determines the locations of fences, which if inserted, ensure the correctness of the TM algorithm under the given memory model. We use FOIL to verify DSTM, TL2, and McRT STM under the memory models of sequential consistency, total store order, partial store order, and relaxed memory order.