GURPS Social Material

GURPS has a rich and detailed social rules system. There are advantages such as Allies, Contacts, and Patrons for getting regular aid from NPCs. Claim to Hospitality, Rank, Status and other more organizational advantages for a more broad range of social influence.
And of course Reaction modifiers such as Charisma, Reputation and others for influencing people (or things) you meet.
Just Roll 3d6 Understanding Reaction Modifiers is a good explanation of the latter.
Normally when you meet someone they have a predetermined reaction but this can be modified by your skills, advantages and disadvantages. A merchant may start of with a Neutral reaction but you could make that better with the right abilities and get a better deal.  The Town Guard may have a hostile reaction to your bar fight but some quick Fast talk or Diplomacy or perhaps higher social status may turn it around so you get off scott free while the other guys get arrested.
GURPS Basic Set includes all the rules you need for this, though GURPS Social Engineering expands this with worked examples and some additional detail.

The GURPS Social Engineering series goes over the social interaction rules in loving detail to provide help in running anything in that vein, Court Intrigue, finding a fence or informant, corporate espionage, or even finding a good party. Additional books in this series include Back to School (Dojos, High Schools, college, and more) and Pulling Rank (Working as a member of an organization).
Boardroom and Curia and City Stats help you build organizations or cities with short easy to read templates. Dungeon Fantasy 17: Guilds is great for building DF guilds.

Blog Posts
Social Advantages
Social Skills

Related Material

Other books are more GM guides that help you run a certain style or build your world.
GURPS Fantasy and GURPS Space give world building guidelines. GURPS Adaptations gives guidance for converting your favorite book or movie to a GURPS setting.
GURPS Mysteries helps with creating and handling player investigation stories. GURPS Cops and GURPS Covert Ops, or Espionage are all good Third edition books that can help.


GURPS Social Engineering: Pulling Rank
Low Tech Companion 1: Philosophers and Kings
Pyramid 3/86: Organizations 
Just Roll 3d6 Understanding Reaction Modifiers is a good explanation of the subject.