Exclusive photoproduction of ρ 0 (770) mesons is studied using the H1 detector at the ep collider HERA. A sample of about 900,000 events is used to measure single- and double-differential cross sections for the reaction γ p → π + π - Y . Reactions where the proton stays intact ( m Y = m p ) are statistically separated from those where the proton dissociates to a low-mass hadronic system ( m p < m Y < 10 GeV ). The double-differential cross sections are measured as a function of the invariant mass m π π of the decay pions and the squared 4-momentum transfer t at the proton vertex. The measurements are presented in various bins of the photon–proton collision energy W γ p . The phase space restrictions are 0.5 ≤ m π π ≤ 2.2 GeV , | t | ≤ 1.5 GeV 2 , and 20 ≤ W γ p ≤ 80 GeV . Cross section measurements are presented for both elastic and proton-dissociative scattering. The observed cross section dependencies are described by analytic functions. Parametrising the m π π dependence with resonant and non-resonant contributions added at the amplitude level leads to a measurement of the ρ 0 (770) meson mass and width at m ρ = 770.8 - 2.7 + 2.6 (tot.) MeV and Γ ρ = 151.3 - 3.6 + 2.7 (tot.) MeV , respectively. The model is used to extract the ρ 0 (770) contribution to the π + π - cross sections and measure it as a function of t and W γ p . In a Regge asymptotic limit in which one Regge trajectory α (t) dominates, the intercept α (t = 0) = 1.0654 - 0.0067 + 0.0098 (tot.) and the slope α ′ (t = 0) = 0.233 - 0.074 + 0.067 (tot.) GeV - 2 of the t dependence are extracted for the case m Y = m p . [ABSTRACT FROM AUTHOR]