TLDR: There are so many viable builds for Swain. It's up to you. But I may be biased here.

Tear rush gives you stronger early lane control in which Catalyst fails to deliver. GLP is still good but it has no HP and Catalyst stat in next patch. You have 20% CDR from Archangel. Abyssal gives CDR and MR, may be a better option than RoA. Zhonyas lost its purpose since you actually want to spam as many spells as possible before you die.

Disclaimer: I am not a low elo/reddit-tier analyst.

Tear

The first question you have to ask yourself before you build Tear - does Swain have mana issue? Some say he doesn't need Tear since Catalyst already gives enough mana sustain. This may be true when you don't spam abilities during laning phase.

Tear actually gives you stronger laning phase - stronger wave control, pokes and cs. Swain is supposed to be a lane-dominant champion. A successful lane control is your duty in your every game. Mana becomes the key here. You want to spam E and AA to poke down enemy. You want to fast push with Q, E when enemy is recalling. You want to use Q to have perfect CS, CS-ing is still hard for Swain.

Clearly, it's hard for Catalyst to support this pattern of mana consumption. Does Catalyst really give your mana sustain before level 6? Not really, because you hardly proc the catalyst mana passive unless you are trolling (you need to be damaged by enemy in order to receive free mana from Catalyst). 300 mana is not comparable to Tear if you want to maintain high pressure over enemy in early game.

You can build into Archangel later which gives 20�r and synergies with Catalyst or other mana items.

ROA vs Abyssal

P: 20-105 ( 30%AP)

Q: 65-145 ( 40%AP)

W: 100-300 ( 70%AP)

E: 35-175 ( 25%AP)

R: 35-65 ( 14% AP) and 15-45 (16%AP)

I would biasedly say that Abyssal > RoA. Abyssal gives you instant HP, mana, 10% CDR and 10% extra damage aura. Swain's AP ratio is crap except his W. Abyssal is strong against AP matchups and gives your team some damage boost. However RoA gives more mana which synergies with Archangel later. RoA also gives more HP.

RoA has a clear advantage over Abyssal when (thanks /u/Trade-Prince):

• enemy is hit by 5 bolts.
• enemy is hit by E twice.
• if you manage to finish your ult before you are dead.

GLP

The new change gives GLP 20% CDR, but it removes HP and Catalyst stats. Building GLP now makes you very squishy in early game, especially if you are rushing Tear. However it still synergies well with Archangel and Glacial Argument.

Zhonyas

You have to ask yourself - why do you need a zhonyas? for survival? for more damage from ult? Survival may be the answer but there is a trade-off. Your R is not giving you enough damage or heal in teamfight as before. Going static for 2 seconds is a waste of time, since you could spam your Q and passive. You rather rush Tear, Catalyst item and Rylai instead of Zhonyas.

You may wanna read about this: https://www.reddit.com/r/SwainMains/comments/7xrqtz/i_dont_think_zonyas_is_core_anymore/

Thanks /u/KaptainKickass!

Runes

Electrocute gives shit tons of damage in lane and in teamfight. Comet gives decent damage but it's hard to hit unless you E them in early game. Aery may be good if you poke enemy a lot in early game, but it's useless in late game. Phase Rush gives you mobility to chase down enemy. However your team probably has enough CC for you to proc damage. Glacial is strong in both teamfight and laning phase. During laning phase, you easily poke down enemy and dodge their trades by Glacial slow. In teamfight, it synergies with GLP well (if you build it). Spellbook allows you to take ignite, so you have strong laning presence and first blood potential in early game. You can switch to tp later.

All runes have been tested by high elo players and streamers. It's safe to pick either one.

Feel free to comment, or input something useful here. So i can update my info.

Feel free to argue with me by saying Tear is a trash item on Swain. It's not, but it's up to you.

Personal preference boys.