Okay, time for Madrid tips. Both Adam and Spyhunter has hit 1:32.1s which means a high 1:31 is feasible. However, my PB is only a 1:32.4 and I'm struggling to hit high 1:32s consistently due to one certain corner.
Just a note, the tires take a fair while to heat up so best times won't be seen until Lap 3 at the earliest. However, that also means you'll get at least 3-4 laps or even more to hit personal bests.
T1 - First off, passing here is very risky and it endangers both cars so save that move for the next two corners. It's very easy to lose focus and bang the wall at the apex. Therefore, it's best to make your braking, downshift, and turning to be nice and smooth instead of charging in and maintaining all the speed you can. Don't slow down too much but do not accelerating exiting because that will upset the car. Line up the car to go either all the way to the left or at most, the middle of the track for the upcoming turns. I've tried going all the way to the outside and I can't get that to work right.
T2 and T3 - Technically, it's two corners but it should be seen as one hairpin. 1st is recommended upon entry. If you lined up the car correctly as stated in the T1 section, you don't need to worry about banging the inside wall so turn in good and early. If wheelspin is occurring at exit, either go 90% throttle and/or shift to 2nd a little early.
T5 through T8 - Your braking point will vary depending on the brake setup. However, it's definitely before the crosswalk that adorn T5 and with cold tires or when following someone, it's better to be gentle with the braking since locking the tires up is very possible here. Brake in a straight line aiming the nose to the curbing adorning the inside of T6. Depending on driving style, you can either let the car drift to the middle between T6 and T7 or hug the inside completely through there. Either way, you should apply less than full throttle throughout here and when going through T7, you'll need to aim the nose towards T8. Practicing getting very close to the wall without hitting it. You may need to lift off entirely to slide the nose properly to avoid the outside wall on exit.
T9 - Gently bring the speed down and hug the inside very tight all the way around, especially on the exit. The car will want to drift out but this will hurt you bad at the next corner. The curbing sometimes help but I've had instances of wheelspin here so it's up to you whether to use it or not.
T10 - Very hard corner as the car pushes like mad on exit. For consistency, as I exit T9, I upshift to 3rd, let off the throttle and slide the nose so that my rights will hit the tall strips on the right and then go around 80-90% throttle until I feel good about my exit and push the gas pedal all the way down. Giving up a little speed on entry will be made up with a solid exit because not only hitting the wall will ruin your lap, hitting the outside strips will actually slow down the car. You can also use 2nd all the way here if that's faster for you.
T12 through T14 - Draw a line from the outside curbing of T12 to the inside curbing of T13. That's roughly your braking zone. Carry just enough speed entering T13 so that the car goes up about two or three lanes and coast the car to the middle of the track. Then, gently apply power and aim for the inside curbing. That should allow you to clear T14 without hitting the wall. This requires a fair amount of practice to get right. If you're worried about someone poking the nose inside of you, only go up one lane and add a dab of throttle to keep the car going before cutting inside again.
T15 and T16 - Oh yes. This is the chicane that is so hard to get right. The time gained or lost here is easily .5 second either way and I'm more often losing than gaining here. Slow the car down nice and easy and keep your eyes on the prize, mainly the curbing on both corners. Aim the car deep to the T15 curbing and when you reach it, jab the nose towards the curbing at T16 while staying off the throttle. Be very careful on when to reapply throttle because you may get severe understeer or you can also get wheelspin on exit. The key, in my view, is use minimal steering throughout the whole complex so you may actually want the car positioned almost all the way to the inside entering so that you almost have a straight approach.