First of all, refer to this for better visualization: http://www.tosbase.com/tools/skill-simulator/
Now let’s start with an example case study.
There are four basic classes in ToS; Swordsman, Cleric, Archer and Wizard. Let’s name them the Rank 1 classes. Let’s say you choose to become the Swordsman. And then, you level up your Swordsman until you are able to advance through the next class, which you can call the Rank 2 classes. Rank 2 classes which branches off from Swordsman consists of three classes; Another Swordsman, Highlander and Peltasta. You probably ask, does the Swordsman in Rank 2 is the same class with the one in the Rank 1? The answer is yes, in fact, Swordsman in Rank 2 is the more powered up version which brings more skills (You can learn two new skills as a Rank 2 Swordsman; Restrain and Pommel Beat). The question is, will you lose the skill you got in Rank 1 Swordsman if you chose to advance to Peltasta or Highlander? The answer is no. You will still carry the skills you got as Rank 1 Swordsman! You must get through Rank 2 to be able to advance to Rank 3, and so on, which answers to your question about whether or not you could skip classes.
But be very careful, in some cases, you wouldn’t be able to use the skills from previous ranks because of weapon restriction. For example, you chose to advance to Rank 5 Corsair after Barbarian at Rank 4. Corsair’s primary weapon is a one-handed weapon coupled with an offensive off-hand weapon, typically, a dagger type weapon. Barbarian is a class which uses a two-handed sword which a lot of its skills require you to equip a two-handed sword. But you can, of course, use buffs that were available at Barbarian skill tree because it has no weapon restriction (refer to the skill simulator).
Hopefully this explanation can give you a better image on how the class and skill system work in ToS. Again, for those who have played or experienced the game, you can, of course correct me if there are slight or major errors in my explanation.