The Pikachu you start with in Pokémon Yellow will not evolve because the Pikachu in question is based on the Pikachu that belongs to Ash Ketchum of the Pokémon TV anime. Ash's Pikachu won't evolve because he likes himself just the way he is and prefers to stay that way rather than chage.
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If this is the case, you're playing Pokemon Yellow. Yellow prevents the starter Pikachu from evolving due to following the anime, where Pikachu refuses to evolve (though it's possible to evolve it by trading it to another game, evolving it there, and trading it back to Yellow).
You cannot evolve Pikachu in Pokemon Yellow, unless you trade it to a red or blue version, and give it a thunderstone there. Once you get it back it will not follow you.
Give Pikachu a Thunder stone and it will evolve into a Riachu. But in Pokemon Yellow, the Pikachu will not evolve. You can get thunder stones easy by mining them in Pokemon diamond and pearl but in soul silver and heart gold you need to buy them with athleet points at the athleet shop
Evolving PikachuPickachu will not evolve in Yellow; it will refuse the Thunderstone, but if you trade your Pikachu from Blue or Red, you can evolve it with a Thunderstone then.
Pikachu do not evolve by level. They evolve when a thunderstone is used on them.