Elder Scrolls V: Skyrim - Guide to Magic Skills and Perks
All magic skills have perks that allow you to half the amount of magicka it costs for the different ranks in a particular magic skill. These are the most important perks to have (especially as a mage) if you want to use a magic skill effectively. As for the rest of the perks, they are all based on your play style (see how to play a mage for more details) and whether or not you find the perk is worth having.
The first branch of the tree (far left) is dual casting which more than doubles the duration and doubles the max levels of your illusion spell. The next branch (second from the left) lists the skills ranks. The next branch (second to last) allows you to upgrade illusions spells based on your traget (increases levels when used against animals and people), along with the ability to cast spells silently (quiet casting). The last branch (far right) upgrades specific illusion spells oin the order that follows: calm, fear, frenzy. The last perk allows you to use illusion spells on creatures that you normally cannot (such as deadra). When deciding perks for illusion, look at the spells that you use most and what perks will allow you to maximize their use (make them as useful as possible).
Conjuration perks are split up into for categories (in order of branches; left to right): Atronach summoning, reanimation, bounding, and overall (the overall is for the ranks associated with this skill). Which perks you get are based on which conjuration spells you use: If you summon atronachs use the first branch, if you conjure undead use the second branch, if you use bound weapons use the third branch, and if you plan on using conjuration a lot then use the fourth branch.
The first three branches in the destruction tree is a choice of specialization. The far left is fire, then frost, and the third one is electric. It goes in order from weakest to strongest (shock being strongest because it takes down both health and magicka), so pick your specialization based on which element you use most (if you use them all evenly you could get them all but that would waste a lot of perks). The next branch after them is the rank branch and the last branch is dual casting, which is suggested because it more than doubles the amount of damage your destruction spells do, killing you enemies quickly (and staggering them if you get the impact perk).
This is the most beneficial school of of magic (for any class) because it gives the ability to heal yourself whenever you want without the need of potions. Restoration is split up into many branches, all of which giving an amazing ability that can benefit most classes. The first branch is respite, which allows restoration spells to not only heal health,, but stamina as well. The second branch st first increases the amount of health you gain and then allows you to do more damage to undead creatures. The next branch allows ward spells to absorb 25% of the magicka that they are hit with. The next branch is the rank branch. The branch after that increases magicka regeneration and allows the character to avoid death once per day. The last branch is dual casting, which is very effective if you use restoration a lot and are willing to drop your guard to quickly regain health.
This school is mostly for magic based characters. The constellation for this skill literally look like a tree. Each rank of alteration allows you to pick more perks from the tree. The branch at novice is alteration dual casting, doubling the duration of alteration spells (most useful for flesh spells). The two branches at apprentice increases a mage's defensive properties. The branch at adept increases the duration of alteration spells. The final branch at expert allows you to absorb 30% of any magicka that hits you.
The tree for this skill is relatively simple. The perks to the far left of the tree are for weapon enchanters. The perks in the center of the tree are for armor enchanters, and the perks to the far right of the tree are those with enchanted weapons that want to get the most out of their usage. If you are both an armor and weapon enchanter, I suggest that you climb the armor tree before you climb the weapon tree.