There are currently 16 garrison levels. Improving a garrison increases its defensive capabilities for Garrison Engagements, and unlocks Technology points that can be used to obtain stat bonuses for corporation members.
Research is accessed by tapping on a Garrison and accessing the Research tab.
The basic unit of Research are Research Units (RU). The more valuable a resource is, the more RUs it provides.
As a Garrison advances in levels, the RU cost to Research it increases.