List of Field Research tasks and rewards

Please, note that there are always only either: specific amount of stardust, or XP, or just one kind of item, or a particular Pokémon encounter for a single task completed, which means only one of following possible rewards is rewarded for single Field Research task completed not all of them!

Current tasks: January 2020
Theme for Field Research tasks in January 2020 is Ice-type Pokémon.

Catching Pokémon related tasks
Following tasks are related to Catching Pokémon through the Encounter Screen. To complete any of following tasks, Trainer has to successfully capture Pokémon, which is either approached in the wild, from Bonus Challenge or reward encounter for other, already completed Research task.

Throwing Poké Balls related tasks
Following tasks are related with performance of throwing any of Poké Balls when catching Pokémon.

Battle related tasks
Following tasks are related with battling in Gyms, Raid Battles, Trainer Battles or Team GO Rocket.

Other tasks
Following tasks are related with Hatching Pokémon Eggs, evolving or power-upping Pokémon, earning Candy with Buddy and other basic game actions.

Trivia

 * If a Trainer encounters a shiny Pokémon as a research reward, said Pokémon will remain shiny until the Trainer captures it. The Trainer is free to run away and re-encounter the Pokémon and it will always be shiny.
 * Upon collecting the reward (which grants the stamp), you can choose not to enter the encounter immediately, but if you tap the reward again, you will immediately be taken to the encounter without warning. However, if you don't have enough Poké Balls to catch it, you can exit and the reward will still be available later. The Pokémon is considered to have spawned when you first enter the encounter. If you exit and return in a Weather that would boost it, it would not be affected. Encounter tasks do not count towards the 3 task maximum once you have collected the stamp, even if you haven't captured the Pokémon.
 * For Nice/Great throw tasks, a higher tier throw will count.