  Pulsar timing arrays offer a probe of the low-frequency gravitational wave
spectrum (1 - 100 nanohertz), which is intimately connected to a number of
markers that can uniquely trace the formation and evolution of the Universe. We
present the dataset and the results of the timing analysis from the second data
release of the European Pulsar Timing Array (EPTA). The dataset contains
high-precision pulsar timing data from 25 millisecond pulsars collected with
the five largest radio telescopes in Europe, as well as the Large European
Array for Pulsars. The dataset forms the foundation for the search for
gravitational waves by the EPTA, presented in associated papers. We describe
the dataset and present the results of the frequentist and Bayesian pulsar
timing analysis for individual millisecond pulsars that have been observed over
the last ~25 years. We discuss the improvements to the individual pulsar
parameter estimates, as well as new measurements of the physical properties of
these pulsars and their companions. This data release extends the dataset from
EPTA Data Release 1 up to the beginning of 2021, with individual pulsar
datasets with timespans ranging from 14 to 25 years. These lead to improved
constraints on annual parallaxes, secular variation of the orbital period, and
Shapiro delay for a number of sources. Based on these results, we derived
astrophysical parameters that include distances, transverse velocities, binary
pulsar masses, and annual orbital parallaxes.
