Elias Silveraxe is the Guildmaster of the Haven Thieves' Guild.  The title of Guildmaster is traditionally the chief position in a guild.  However, Elias actually answers to one other person, Thalin.  

Elias is the upfront manager, making sure that all of the spoils come into the guild and that tributes are paid on time.  He is the face of the guild and on matters of day-to-day operations he has the final say.

It's the guild's unique areas of influence where he defers to Thalin.  The Haven Thieves' Guild has funneled a portion of its funds into providing for the downtrodden in its territories.  Whether that is keeping murders off the streets or handing out some food, the Thieves' Guild does take care of its own.

Elias is often stern, though he does have a light-hearted side.  Much of his seriousness comes from being the guy who has to make tough decisions.  But, if you spend some time with him you notice that there is a deeper rooted gruffness, possibly to do with something in his past.

There is a famous dwarven merchant family called the Silveraxes.  Many thieves in the guild speculate that he somehow lost honor with that family and now finds his family here with his close friends, Thalin, Elysia, and their adopted daughter, Autumn.