Just some forward notes:
- this build is completely theoretized, as my gaming laptop is currently broken and even if it wasn't, I've already rerolled once (from my useless NB) to a pyromancer, and since exping on the same quests over and over is not even remotely funny (especially among hordes of bots), I do not even want to try this build myself at least till fall

- this is a PvE build. I don't play PvP and I honestly don't give a damn about performance there, but I guess this build could be good enough there.. especially with Vampires vanquished.

That being said, let's start. Here's the build, with more abilities taken than fits in the bars, because you'll want to change your loadout for some specific things:
esocalc.com build

Weapon: Bow/Bow

- I know, I know, right? But we're making an archer, and that's hard to do without a bow

- You'll want to take Poison Injection instead of Venomous Arrow, because thanks to the wonderful interrupt mechanics and projectile speed, chance of actually successfully interrupting is minimal (only working on REALLY long casts). But it's your hide, you can freely take Venom, the difference in DPS is not really that high even in boss fights.

- Magnum Shot is a nice little ability that allows you to kite root(Bombard)-immune (that usually means FLYING) enemy (single, sadly no AoE pwnage). Probably won't be on your bars all the time because Bombard is simply better, but it's the only thing working on flyers, so be sure swap it before engaging a larger group of them or an elite. Also works wonders for soloing world bosses, as most of them aren't immune to knockback, even if they are to root.

- Bombard is the cheapest soft CC you can get, and since most of your other skills use magicka, you can use it quite a few times (provided you have enough stamina and didn't place all your attributes and enchants to magicka and HP

Magic Skills:

- Crystal Fragments - well, you won't be spamming that ofc, to conserve your magicka (and avoid deadly cast time), but every other magicka skill has a solid chance to make it instant and cost just half the magicka (which means still pretty much, it's one bad magicka eater). Doesn't make that much sense in AoE situations, so you'll want to only have it on your Single-target skillbar.

- Summon Charged Atronach - for those.. difficult.. conversations... ehm, I mean.. fights. Situational, not on bars by default

- Velocious Curse - might not sound like much, but it's 2/3 of crystal shard's damage for 2/3 crystal shard's magicka cost, while also dealing solid AoE by explosion. Very much needed for AoE fights, as it's the only cost effective ranged AoE you have.

- Bound Armaments - increases armor (to the cap or almost there), while also increasing HEAVY attack damage (which effectively ignores cap restrictions)

- Power Overload - aka the coolest spell in game - covers your hands with electric charges (infinitely long out of combat, still pretty long in combat), while changing your meager bow attacks into a deadly AoE barrage of electricity (shortens the range to half though), beefs up attack damage (which will be beefed up even more by Surge and Bound armor), turning your left mouse button into a bloody carnage. ALSO, WHILE IT'S ACTIVE, YOU HAVE ACCESS TO 5 MORE SKILL SLOTS which overwrite your current slots (aka you can set 5 abilities to have with Overload off and another 5 abilities with overload on). We'll talk further about that later.

- Mage's Fury - not worth morphing as both morphs are totally useless (unless the damage scales further by morphing, in which case go ahead and pick whichever, the magicka return is really minimal and the bosses rarely have adds around when they are low). But it's a good (aka the only) skill to cast when boss is at 20% or less.

- Surge - Take Critical morph if you think you'll be critting enough, or the other for boss fights as it lasts longer. Your choice. Critical still might be better choice. This is going to beef up your weapon damage to the cap (or almost), grouped with Bound armor and overload it's going to kill (and higher damage on Poison Arrow or Arrow Spray helps a tiny bit too)

- Ball of Lightning - sorcs can simply turn invulnerable.. stunning melees around you, while also escaping from them, while also making yourself absorb any spells (+ ranged attacks of which most - except light and heavy attacks - are counted among spells). Totally worth the magicka.

Passives at this point should give you:
- 5% reduction of stamina and magicka costs
- Crystal Fragments heal you for 5% max HP and make target 15% more susceptibe to criticals for 2 seconds
- cost of ultimates reduced by 15%
- health regeneration increased by 20%
- magicka regeneration increased by 10%
- storm abilities have 5% more damage
- lightning spells have 10% chance to instakill targets under 25% HP (bosses are immune and it doesn't make much of a difference against normal mobs though.. might save your life one day though)
- storm abilities 10% cheaper
- bow attacks hit distant targets 12% harder
- bow critical chance increased by 5%
- stamina cost of bow abilities decreased by 20%
- bow attacks deal 15% more damage to vulnerable targets (not much use in soloing)
- movement speed upped by 30% for 2 seconds after roll dodging (yay, essentially makes roll dodge work as double roll dodge)


Armor:
- either 5 light 2 medium (for 6% more bow crit for Critical Surge procs) or plain 7 light. You'll get more armor rating from Bound armor, so get whatever you feel you need more. Light armor benefits this build way more in may opinion though.

Other abilities:

- Soul Assault - unparallel single target damage. Ideal (= a must) for boss fights where you don't have to tank. Otherwise you're better off with an atronach

- Evil Hunter - the single most useful ability for any undead and daedric enemies.. which means 90% of the main quest, plus whole Coldharbour zone. Makes Septima Tharn or Molag Bal fights a walk in the park, as you can just spam empowered Bombards to kill the whole armies they summon in SECONDS). Otherwise zero usefulness, so put it on bar only when fighting undead&daedra.

- Degeneration - IF they're going to buff it enough, and IF they're gonna fix it's trigger effect. So far not worth.

Race:
- breton (master race), or altmer, don't even dare using some other race, it's simply not worth it for casters



Skillbar1 (single target dps):
Bow
1 Crystal Fragments (used mainly when it procs)
2 Poison Injection/Venom Arrow (to burn stamina)
3 Velocious Curse (magicka ability to proc Crystal Fragments, high damage, but can only be used every 3.5 sec, otherwise I guess it refreshes itself and never explode)
4 Mages Wrath (for last 20%, also should proc Crystal Fragments)
5 Bound Armaments
U Soul Assault

Skillbar2 (AoE/soloexping, with Overload off)
1 Velocious Curse (can only be on one target, make the AoE explosion count)
2 Ball of Lightning (CC+defense)
3 Bombard (stamina based AoE root for 3 sec followed by 3.5 sec snare for 40%)
4 Critical Surge (1 bar is enough as it's a buff, not toggle)
5 Bound Armaments
U Power Overload

Skillbar3 (AoE/Soloexping, with Overload on)

whatever you choose, I still haven't managed to find out whether you can use weapon abilities during overload or not (since you use hands to cast it and weapon disappears), so it's probably for the best to at least swap Bombard with Shattering Prison.

Sets:
3x Warlock (if you're willing to go over cap with pure warlock jewelry that can't be reenchanted from useless magicka regen and so lose 3 potential enchants, otherwise don't try)
5x Night Mother's Gaze or Spectre's Eye





Please if you have any relevant comments to the build, share them. This is just plain theorycrafting so feel free to "point out the obvious" so we can improve this build.