Quests are found by spinning stops. You can have a maximum of 3 quests at one point at the same time.
Using the o!quests command, you can take a look at your quests, and dispose of any with the supplied reactions.
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There is a 7-day research reward just like in PokemonGo;
You can capture Legendaries with this method.
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There are also Special Researches. The first one is set up as a Tutorial Research.
After completing that one, you will start working on a Mythical Discovery and others.
You can take a look at your available Researches with o!research
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Some special researches can be completed again by using a Researcher Stone