Two-sided mobility platforms, such as Uber and Lyft, widely emerged in the urban mobility landscape. Distributed supply of individual drivers, matched with travellers via intermediate platform yields a new class of phenomena not present in urban mobility before. Such disruptive changes to transportation systems call for a simulation framework where researchers from various and across disciplines may introduce models aimed at representing the complex dynamics of platform-driven urban mobility. In this work, we present MaaSSim, a lightweight agent-based simulator reproducing the transport system used by two kinds of agents: (i) travellers, requesting to travel from their origin to destination at a given time, and (ii) drivers supplying their travel needs by offering them rides. An intermediate agent, the platform, matches demand with supply. Agents are individual decision-makers. Specifically, travellers may decide which mode they use or reject an incoming offer; drivers may opt-out from the system or reject incoming requests. All of the above behaviours are modelled through user-defined modules, allowing to represent agents' taste variations (heterogeneity), their previous experiences (learning) and available information (system control). MaaSSim is a flexible open-source python library capable of realistically reproducing complex interactions between agents of a two-sided mobility platform. MaaSSim is available from a public repository, along with a set of tutorials and reproducible use-case scenarios, as demonstrated with a series of illustrative examples and a comprehensive case study.