There is no class-based leveling system in EVE. Instead, there is a very extensive skill system. Players choose from a wide variety of skills. You can train up to five levels in each skill, each with a number of sub-levels. Characters start with skills they selected during character creation and may also buy skill-training kits, which are sold like any other commodity, then rigged neurally to the character, much like knowledge is gained by the characters in "The Matrix."" Skill-training kits vary widely, both in price and availability. Once you learn a skill, you cannot unlearn it - but you don't need to. There is no limit to the number of skills or skill points a single character can attain. 

Skill advancement
Character advancement is accomplished through the activation of skill training kits. Once a training kit is utilized, a certain period of time must elapse before training is complete and the skill is functional. The activation time required is measured in real time and training continues regardless of whether or not a player is connected to the game. The training time needed for skills may range from less than an hour to several days, depending on the type and complexity of the skill. You may only train one skill at a time and only on one character at a time per account. Time elapsed during training may be monitored through the character sheet.

You may purchase skill packs through the market either from players or NPCs. The cost and availability will vary, based on the supply and demand of the skill.

Obtaining all skills
The likelihood of an Eve Isk character being fully trained in all available skills is virtually zero and not something that could be easily achieved. Advancing a skill, particularly at the higher levels, takes time and new skills are introduced occasionally as the game grows and additional features are introduced. Estimates have indicated that it could take as long as three years for a character to be at the top level of all available skills. By that time, many more skills will have been added.

Though it may seem like gaining skills could be a grueling process, the unique training system in Eve Isk is unheard of in other MMORPGs and contributes greatly to EVE's appeal.