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So, I bought the book, read it, but I have a question, and just to be sure:
The max level from an skill in rank can't be more than your level, so, a starting character can only have a skill on level 1 rank, right?
Later in the book, it says that the max rank on a skill can't be more than your hit dice, so, for example, a bard has a d8 hit die, so, does that means he can only rank his skill up to 8, once he leveled up once?
As you state correctly, a character can have a maximum number of skill ranks in any skill equal to its Hit Dice.
Hit Die, singular, (i.e. the bards d8) is a basic component of a class and only determines the amount of hit points a character gets upon taking a level in the class1. It is (hopefully) never abbreviated HD.
Hit Dice (or HD), plural, means the number of hit dice you have, not the size of the die itself. For regular characters (e.g. standard races), this is equal to the total amount of class levels he has, i.e. his character level.
Monsters also have Racial Hit Dice, which are added to all class levels they possess (if any) to determine their Hit Dice2.
In statblock notation (like in the Bestiaries), it is noted as XdY+C, where X is the Hit Dice, Y the Hit Die, and C all constants (CON-Bonus, Toughness, etc.). If there are more than one type of Hit Die, there are more terms like the first one. The total Hit Dice of the creature then is the sum of all Xs.
Some quick Examples:
4d8+C4d12+8d6+C2d8+7d10+C1 The hit die also usually determines the BAB progression of the class. This holds true for all Paizo classes as of this moment, but not all 3PP classes follow this trend.
2 For a more thourough explanation, see Jack Lesnie's Answer
This is because Racial Hit Dice means that for some (usually Monstrous, non-standard) races, your total Hit Dice is not the same as your Class or Character Level.
Quick Guide;
Hit Dice - can be Racial or from Class levels. Gives varying skillpoints depending on type, varying rates of BAB, varying rates of base saving throws, and determines the dice size for rolling hitpoints
Class Level - your level in a specific class. Each level in a class adds a hit dice, plus possibly class abilities (like bonus feats, or spells, or sneak attack).
Character Level - A combination of all your class levels (different from class level because Multi-classing can lead to different levels in multiple classes).
Effective Character Level (ECL) - A combination of all your racial hit dice, levels in classes, and LA (Level Adjustment) to get a single number. This is important for determining experience levels and what 'total level' the character is. The idea is that races like Ogre etc that are great cost a number of racial hit dice and level adjustments compared to 'regular' races like Human, but need to be in the same party as Humans etc, so even though they only have 5 levels in classes compared to the 11 levels the Human has (as they spent 6 levels on Level Adjustment and Racial Hit Dice to play their race), they still count as a level 11 character for experience points etc.
Max skill ranks are based on total hit dice, so unlike ECL (Effective Character Level), it doesn't count LAs (Level Adjustments) in that total. So a Level 11 (ECL 11) character with 4 LA (from being a Half Vampire or something with 4 Level Adjustment, I don't know what has that), would only be able to put 7 ranks into skills (11-4). Whereas a character with ECL 11 made entirely out of levels in classes would get to put 11 skill rank into skills. Or one with ECL 11 made out of class levels and Racial Hit Dice.
Hit dice are expressed as dY, or more properly XdY, where X is your level. You can not have more than X ranks in a skill. Y is just the highest number of hit points you can roll when you gain a new level. For instance, a 1st level bard would have 8 hit points from his hit die, and would be able to train a number of skills with 1 rank each.
As expressed by other answers, the term "Hit Dice" is equivalent to "Character Level" for Player Characters most of the time (except for monster races, templates, or other stuff you don't need to worry about right now).
It should also be noted that you get an automatic +3 on your roll for any Class Skill that you have ranks in.
So a level 1 Rogue with Dexterity 20 and a single rank of Disable Device will have:
+1 (for the rank)
+3 (Class Skill bonus)
+5 (Dex Bonus)
For a total of +9 at level 1. Not bad.
