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 3p partial waves with J(PC) = 0(-+) ,1(++) ,2(-+) ,2(++) ,and 4(++). In these waves, we observe the well-known groundstate 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).