When looking up my future AUS-SEA RT, I found this on ExpertFlyer. Could someone go over it with me and explain possible routings I could take to maximize mileage?

V FARE BASIS BK FARE TRAVEL-TICKET AP MINMAX RTG
1 TA14A0NA T X 109.00 ---- 14/1 -/ - 169
PASSENGER TYPE-ADT AUTO PRICE-YES
FROM-AUS TO-SEA CXR-DL TVL-02MAR12 RULE-9050 DFR/11
FARE BASIS-TA14A0NA SPECIAL FARE DIS-N VENDOR-ATP
FARE TYPE-SIP OW-INSTANT PURCHASE
USD 101.40 0169 E19JAN12 D-INFINITY FC-TA14A0NA FN-
SYSTEM DATES - CREATED 19JAN12/1538 EXPIRES INFINITY

PUBLISHED RTG AUS-SEA/DL169 /TAR-DRG1 EF-19JAN12 DIS-INDEF

1. AUS-LAX/MEM/MSP/SEA/SLC-SEA
2. AUS-SEA

I am currently AUS-MSP-SEA-SLC-AUS

You can fly AUS-SEA non-stop. (AS codeshare?)

You can make a single connection in LAX/MEM/MSP/SEA or SLC between AUS and SEA.

That's the universe of routings for that specific fare.

Routing allows one connection, which can be in LAX, MEM, MSP, or SLC. Feed your segments into the Great Circle Mapper and discover that MSP beats MEM by 10 miles. You can increase mileage by ~650 by connecting in MSP or MEM instead of SLC.

I particularly enjoy the prospect of making my one connection en route to SEA in SEA. Who writes these rules?

Hard to say! I pasted it, so it's not my poor keyboard skills responsible for the error.

How do you determine the number of legal connections?

So, by this, I could not do, say, AUS-MEM-LAX-SEA?

Nope, if you could do that, you'd see AUS-MEM-LAX-SEA (or maybe AUS-MEM-LAX/MSP-SEA or AUS-MEM-LAX/MSP/SEA-SEA) in the list. A connection point is surrounded by - -, and / indicates you can pick one of those points for the connection.