The Arcane Bladesman
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The Arcane Bladesman is a specialised mage who utilises a bound sword in his right hand and another spell in his left hand. He wears robes, which give him boosts to his magical abilities, but uses the alteration school of magic to temporarily improve his armour rating when in trouble. Carrying no physical weapons and wearing no armour, this mage is a light a nimble character that is very versatile and, once properly equipped, capable of tackling most foes with ease.
Best Race For This Build
All of the races within Skyrim are, for the most part, fairly equal and so any race could theoretically serve well for this build. But, looking at their base attributes, an Altmer/High Elf is naturally the best for any character who wields magic. However, I picked a Breton because I prefer to play as human races but still wanted a race decent with magic from both an attribute and lore perspective, so the choice is entirely up to you.
Skills To Invest In
Conjuration: Since you will be utilising a bound sword almost all the time, it is important to place perks into the Conjuration school of magic. Enough so that you at least have the "Mystic Binding" perk which allows you to deal more damage with bound weaponry. Should you want to summon atronachs or familiars, there also a host of perks available for you within this skill tree.
One-handed: Naturally, as you will be utilising a one-handed sword (albeit not actually physical), you'll be earning levels within and also wanting to put perks within One-handed weaponry. The most important perk, in my opinion, is "Armsman" so that you can deal extra damage with the bound sword. Should you want to dual wield with two bound swords, which is easily doable, there are also other perks available in this tree that you may want to take.
Alteration: Wearing robes, whilst offering some good bonuses towards magic users, leaves you rather volatile with no armour. Using the Alteration skill tree, you can improve the effect of spells that can temporarily give you up to 60 armour rating. Since these spells can simply be continuously cast, this allows you to effectively be wearing armour as such.
Destruction: You don't really need to put any perks into this, but simple destruction spells are good for some ranged attacks and so I felt the need to bring this up. Perks such as shock allow you also to drain magicka, which is great for tackling magic-wielding characters (something that you will be doing a fair amount of within the College of Winterhold quests, which I recommend doing early on to get some good robes).
Restoration: In my opinion, Restoration is essential for any character build simply to heal yourself. But, with the release of Dawnguard on the Xbox 360, you can become a vampire lord. Many vampires within the game use conjuration, so I think being a vampire works well with this build. The problem is that, once you reach level 4 vampirism, you stop regenerating magicka, stamina or health in the sun until you feed again. By wearing robes that increase magicka regeneration, this can be negated by then investing into Restoration perks which allow you to regain both stamina and health when healing.
Things To Consider
You could, in theory at least, swap one-handed weaponry for archery and then utilise the Illusion perk "Quiet Casting" whilst investing in Sneak and using a bound bow instead of a bound sword. With this, you then have a capable stealth mage. Not sure how it'd work, as I simply hate playing stealthily, but it is something you might want to try.
The College Of Winterhold Quests
You get some semi-decent robes just for signing up to the college, so I recommend doing this.
Give Me Your Opinions
Feel free to leave me some feedback, which I may incorporate into my revisions to this build. Thanks for reading this also!