In this paper, we present a new Matlab-based toolbox for power system analysis, called MatDyn. It is open-source software, and available for everyone to download. Its design philosophy is based on the well-known open-source Matlab toolbox MATPOWER, but its focus is transient stability analysis and time-domain simulation of power systems, instead of steady-state calculations. MatDyn's philosophy, design criteria, program structure, and implementation are discussed in detail. A trade-off is achieved between the flexibility of the program and readability of the code. MatDyn retains overall flexibility by, for instance, allowing user defined models, and custom integration methods. The software is validated by comparing its results with those obtained by the commercial grade power system analysis package, PSS/E. Despite the fact that MatDyn is fairly new, it has already been extensively used in research and education. This paper reports interesting results obtained with MatDyn in recent research that would be hard to obtain using commercial software.