This paper presents the gamma-ray spectral and timing results from the long-term regular observations of Mrk 421 with the Large Area Telescope (LAT) onboard Fermi during 2008 August–2023 August. We discerned six periods of the relatively stronger 0.3–300 GeV activity compared to other time intervals. The baseline brightness level varied on timescales from several months to years during these periods, which was superimposed by shorter-term flares of the different asymmetry. The latter are explained by various interplay between the light-crossing, particle acceleration and cooling timescales. The source also frequently exhibited two-peak flares, to be triggered by the propagation of forward and reverse shocks after collision between the “shells” of high-energy plasma, moving with different speeds down the jet. The strongest long-term flaring activity was recorded during 2012 June–2013 October and 2017 October–2018 March when the source was mostly brighter than $10^{-7}\text{ ph}\,\text{cm}^{-2}\,\text{s}^{-1}$ in the 0.3–300 GeV energy range and robustly detectable even on intraday timescales. We detected 25 instances of intraday variability and a large number of the flux doubling/halving instances, allowing to constrain the upper limit to the emission zone size to be in the range of $1.3\times 10^{16}\text{ cm}\text{--}1.1\times 10^{18}\text{ cm}$ . The source generally showed a lognormal variability in the LAT energy range, explained as an imprinting of the disc nonstationary processes on the jet, proton-initiated hadronic cascades or random fluctuations in the particle acceleration rate. Most of the 0.3–300 GeV spectra were well-fit with a simple power-law model and showed a very broad range of the photon-index from $\Gamma \sim 2.8$ down to $\Gamma \sim 1.2$ , with the mean values $\Gamma _{\mathrm{mean}}=1.75\text{--}1.84$ and distribution peaks $\Gamma _{\mathrm{p}}=1.73\text{--}1.82$ during the periods of strong LAT-band activity. Our spectral study also revealed the features of inverse-Compton upscatter of X-ray photons in the Klein-Nishina regime, relativistic magnetic reconnection, first-order Fermi mechanism within the magnetic field of different confinement efficiencies and stochastic acceleration.
