Solar flares are the most energetic events in our Solar System. They consist of sudden energy release from reconfiguration of magnetic fields, leading to acceleration of particles to relativistic energies. The Fermi Large Area Telescope (LAT) gamma-ray observations of the Sun present a unique opportunity to explore the mechanisms of high-energy emission as well as particle acceleration and transport in solar flares. I will present the results of the first 9 years of observations of the active Sun by the Fermi-LAT, which represents the largest sample to date of detected solar flares with emission greater than 30 MeV. Some of the new detections confirm the standard models for solar flares based on observations from past missions in the 1980s and 90s, but new behaviors have also been identified: detections of delayed gamma-ray emission lasting up to 20 hours and the first detection of gamma-ray emission above 100 MeV from three solar flares originating from behind the visible part of the Sun. Considering all of the 46 flares detected by the Fermi-LAT, I will describe the characteristics of the first gamma-ray solar flare catalog covering Solar Cycle 24, exploring trends and correlations with the most relevant solar events: X-ray emission, coronal mass ejections, and direct detection of solar energetic particles.