  The COMPASS collaboration has collected the currently largest data set on
diffractively produced $\pi^-\pi^-\pi^+$ final states using a negative pion
beam of 190 GeV/c momentum impinging on a stationary proton target. This data
set allows for a systematic partial-wave analysis in 100 bins of three-pion
mass, $0.5 < m_{3\pi} < 2.5$ GeV/c$^2$ , and in 11 bins of the reduced
four-momentum transfer squared, $0.1 < t < 1.0$ (GeV/c)$^2$ . This
two-dimensional analysis offers sensitivity to genuine one-step resonance
production, i.e. the production of a state followed by its decay, as well as to
more complex dynamical effects in nonresonant $3\pi$ production. In this paper,
we present detailed studies on selected $3\pi$ partial waves with $J^{PC} =
0^{-+}$, $1^{++}$, $2^{-+}$, $2^{++}$, and $4^{++}$. In these waves, we observe
the well-known ground-state mesons as well as a new narrow axial-vector meson
$a_1(1420)$ decaying into $f_0(980) \pi$. In addition, we present the results
of a novel method to extract the amplitude of the $\pi^-\pi^+$ subsystem with
$I^{G}J^{PC} = 0^+ 0^{++}$ in various partial waves from the $\pi^-\pi^-\pi^+$
data. Evidence is found for correlation of the $f_0(980)$ and $f_0(1500)$
appearing as intermediate $\pi^- \pi^+$ isobars in the decay of the known
$\pi(1800)$ and $\pi_2(1880)$.
