Fallout primary statistics

Overview
The minimum for each primary statistic is 1 and the maximum is 10. These boundaries can never be broken, even with bonuses or maluses. Each statistic directly modifies certain derived statistics. In addition, every skill is tied to a primary statistic. Some perks require certain minimum attribute values as well.

Increasing attributes
You can get a doctor in the Brotherhood to perform operations on you to raise each of your stats (except luck) by 1, although this is really expensive. Wearing Power Armor will also raise your Strength by 3.