Solar Orbiter, the first mission of ESA's Cosmic Vision 2015-2025 programme and a mission of international collaboration between ESA and NASA, will explore the Sun and heliosphere from close up and out of the ecliptic plane. It was launched on 10 February 2020 04:03 UTC from Cape Canaveral and aims to address key questions of solar and heliospheric physics pertaining to how the Sun creates and controls the Heliosphere, and why solar activity changes with time. To answer these, the mission carries six remote-sensing instruments to observe the Sun and the solar corona, and four in-situ instruments to measure the solar wind, energetic particles, and electromagnetic fields. In this paper, we describe the science objectives of the mission, and how these will be addressed by the joint observations of the instruments onboard. The paper first summarises the mission-level science objectives, followed by an overview of the spacecraft and payload. We report the observables and performance figures of each instrument, as well as the trajectory design. This is followed by a summary of the science operations concept. The paper concludes with a more detailed description of the science objectives. Solar Orbiter will combine in-situ measurements in the heliosphere with high-resolution remote-sensing observations of the Sun to address fundamental questions of solar and heliospheric physics. The performance of the Solar Orbiter payload meets the requirements derived from the mission's science objectives. Its science return will be augmented further by coordinated observations with other space missions and ground-based observatories.

The Solar Orbiter mission