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If you are an elf, you are proficient with the longsword, regardless of class. A wizard, for example, is not normally proficient with the longsword, but an elvish wizard is proficient with all the weapons listed in the description of the elf race. Class weapon proficiencis stack with race weapon proficiencies.
A fighter is proficient with all martial weapons. The Elven Curve Blade is an exotic weapon, except for an elf - the elf considers it a martial weapon, so an elf fighter is proficient with the ECB, but a human fighter is not.

Dread Knight |

I'm a little confused with the Pathfinder Corebook's system in weapon proficiency. Are Race's weapon proficiency still applicable to any class? Say, I want to be an Elf Wizard. The Elf is proficient in Longsword, can I still wield a Longsword as a Wizard? Please let me know ASAP! Thanks!
If it says you are proficient then yes you can use it; if it says treat it as a martial weapon than no you are proficient with unless you can use martial weapons.
Weapon Familiarity: Elves are proficient with longbows (including composite longbows), longswords, rapiers, and shortbows (including composite shortbows), and treat any weapon with the word “elven” in its name as a martial weapon.
So as a Wizard you can use longbows, longswords, rapiers, and shortbows along with the Wizard's normal proficiency but you can't use say an Elven Curved Blade unless you had Martial weapon proficiency. Same for Dwarves with axes, hammers, and picks.

Lost In Limbo |

Yes, all proficiencies are additive. You can use all weapons on the wizard list and all weapons on the elf list witout penalty.
The only exception is the "and treat any weapon with the word “elven” in its name as a martial weapon." line, which simply makes those weapons which are usually classed as Exotic simply Martial for you.