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Pulsar timing arrays (PTAs) are ensembles of millisecond pulsars observed for years to decades. The primary goal of PTAs is to study gravitational-wave astronomy at nanohertz frequencies, with secondary goals of undertaking other fundamental tests of physics and astronomy. Recently, compelling evidence has emerged in established PTA experiments for the presence of a gravitational-wave background. To accelerate a confident detection of such a signal and then study gravitational-wave emitting sources, it is necessary to observe a larger number of millisecond pulsars to greater timing precision. The SKA telescopes, which will be a factor of three to four greater in sensitivity compared to any other southern hemisphere facility, is poised to make such an impact. In this chapter, we motivate an SKAO pulsar timing array (SKAO PTA) experiment. We discuss the classes of gravitational waves present in PTA observations and how an SKAO PTA can detect and study them. We then describe the sources that can produce these signals. We discuss the astrophysical noise sources that must be mitigated to undertake the most sensitive searches. We then describe a realistic PTA experiment implemented with the SKA and place it in context alongside other PTA experiments likely ongoing in the 2030s. We describe the techniques necessary to search for gravitational waves in the SKAO PTA and motivate how very long baseline interferometry can improve the sensitivity of an SKAO PTA. The SKAO PTA will provide a view of the Universe complementary to those of the other large facilities of the 2030s.