Mitigation refers to activities to prevent or at least limit the magnitude of dangerous climate change, mainly by reducing the emission of greenhouse gases and enhancing the sinks. Climate change as a scientific concept went through different phases. At the beginning, then still called global warming, the discourse was if it is happening at all. Some scientists at that time warned of a new ice age (cooling rather than warming of the climate) and those talking about the possibility of global warming were often displayed as unserious. The next phase was dominated by the idea that climate change was happening, this now became scientifically accepted and concerns were of how to prevent it from happening. Here mitigation was given greatest importance. The major event of this phase is the Kyoto Protocol, aiming to bring down greenhouse gas emissions to a level that dangerous CC could be averted. The present paradigm is that mitigation, even if successful, cannot avert climate change, as CC is nothing that might happen in future, but it already has started. As a result much more emphasis is given to adapt to (and also cope with) CC. This paradigm does not eliminate mitigation, but science now assumes -as mentioned above- that even drastic mitigation efforts would come too late to prevent CC from happening, but in the long-run mitigation still can reduce the impacts. Mitigation is the reduction in the generation of greenhouse gases, enhancing the capacities of sinks. What the first is concerned means shifting to other, non-carbon-based energy, increase efficiencies in energy consumption and production, change societal organization that lesser energy is consumed, etc. Enhance the capacities of sinks refers to re- and afforestation, storing carbon in geological formations, etc.
The many reports of the IPCC give the state of scientific knowledge in a very great detail on many aspects of mitigation.
However, we are now stuck as there are few alternatives that are ready to use. So, be prepared to face the consequences of this extra CO2 and methane in the air.