Okay so here is an experimental game I played earlier today. It was not my best play but I had a lot of fun.
However, I take away from this game that I really need to work on fending of invasions. I's been a weakness of mine since forever. If an opponent invades, he'll live, even if I'm super strong in the neighbourhood.

So both for the upper and the bottom side. Can someone please tell me
- what I'm doing wrong?
- what/how should I play?
- how can I get better at invasions / fending off invasions?

It'd be very appreciated!

For the top side, I think up until 41 you get a perfectly fine result. 42 at n18(or 44, but I would take 42), or m16 if you want to be absolutely sure to capture(but its worse for points) and you are doing well.
Your 44 is a resonably large mistake(as you saw) and then 50 is a big mistake too that was not punished. You are already connected there, there is no need to take gote!
And of course this atari on 2 stones is gote, he shouldnt defend there at all. Even taking the 2 stones would still be gote.

Same theme on the bottom, count liberties and dont blunder your stones. Instead of the almost-self-atari 130, just connect at n3 and I see only one eye for him (if he goes l2 you can play j3)

Do you think this applied on the top side?
Do you think this applied on the bottom side?

Hint:

I figured he could live on the top side, and I just wanted a big wall in exchange. So maybe the top was not so terrible (except for some mistakes).
Because I wasn't super strong on the top, he could exploit weaknesses.

The bottom should've been stronger. I think an invasion should fail there. Perhaps I am mistaken, though, and I should've just kept him living small.

I see it now.
I was afraid of connecting and him getting L2, but you can falsify that one eye, you're right.
Thanks!

Indeed, from move 19 to 29 it was black who was giving a wonderful example of your title "Invasions - what not to do". Your position at 29 is considerably better than it was at 19, black's invasion helped you build a nice wall and fix your weaknesses for meagre territorial gain.

I hinted to identify your weaknesses, it's a good idea to do this when your opponent invades (and other times!) and make a list. So at move 19:
- white f17 to f14 is a 2 space jump, this isn't connected. One space jumps are usually hard to cut (e.g don't need to worry about o15, plus you have q14 for support), but a 2 space jump is thin so should set a little "warning, cut possible" light flashing in your brain. (In fact this thinness means e18 was an overplay but black let you get away with it, d18 block should have been around c13, your e18 should have been around d14 directly, but maybe you thought you could bully a weaker player). Black could play f16 g16 f15 g15 and then cut at g17 or g14. More stylish ways of cutting like f16 g16 g15 also possible.
- the top is open at o18, so black can jump in at n18 or m17 is sente to connect
- right white group is pretty healthy, but there is some weakness at p15, or black could get a peep at n15
- top left group is less healthy due to the thinness of 2 space jump, black could also play f15 to start chopping it up.
- neither group has 2 eyes, but no need to make them for a while.
- black g18 is threat to connect to corner so might be handy in making eyes on top, but white d19 likely a sente defence against that.

So when black invaded for 19 the above analysis is the sort of thing you should do before deciding how to continue (at least the first 2 points for a 10k). You then capped at 20, this is a fine move, attacks black whilst loosely connecting your 2 groups. But did you consider tenuki? When weak players play bad invasions in small areas of the board, it is often a powerful idea to just play somewhere else bigger (and it's funny and can give you a psychological advantage). How about an empty corner, maybe that's bigger than the cap? Let's say you play d4, and then black jumps at k14, and you play q4, do you feel sad he got to jump? I'd feel pretty happy to get the first move in 2 empty corners. What I would feel sad about is my 2 white groups being separated, so I like capping to connect them (attacking black is secondary).

For 21 black continued inside, as I'd expect a human kyu player to do, but tenuki was probably better. Your f16 answer was good, black just helped you fix that 2-space weakness I was banging on about. Remember to say "thank you" to black. Ditto for the following few exchanges, what a lovely wall. For move 30 there's a decision, do you play your move, which is nice to short black's liberties and reduce his eyespace (and make some for you, also if black descended at g18 it is sente to connect to corner, though your d19 can prevent that in sente), or o18 to disconnect there, or tenuki? All seem plausible to me, though something good about o18 is it disconnects the top right black corner so later s15 is maybe sente for you. If I was black for 31 though I would be sorely tempted to play o18 to connect and give up on the junk g17 stones.

k15 does hurt black's liberties, but also helps him as now you can't cut at h17. L16 is good. L17 is ok, but also think about tenuki. The k18 cut is a mistake though and a very important technique lesson: when you cut like this and the opponent captures they get eyes. So the principal is to cut the side you don't want. Cutting on the inside here means black lives, and then you can capture the m17 stone in gote afterwards (if you didn't make the m19/n17 blunder). Is m17 big and worth spending gote on? A BIG NO. So cut the other side (m18): if black captures this then k18 and j17 captures black in shortage of liberties and is fairly large (but I still prefer an empty corner, so just play there instead of L17). If when you m18 black decides he doesn't want the inside group to die and connects at k18, then you can capture the outside stone with m16. And now the crucial point is black doesn't have as good eyeshape inside because you didn't give him a ponnuki. Does black need to spend a move to live? I leave this as a reading exercise (but with k18 first there is no reading exercise, it's super alive already). Scachus mentioned n18 or m16 later, I strongly prefer m16 for the better aji to the centre.

P.S. for move 20 my favourite move is b15 and d15 atari, this helps fix the 2-space thinness somewhat (black can't cut after f16/f15 combo because white can then capture them) in sente , then I might cap or play an empty corner.

Interesting analysis.
I did notice some of my weaknesses, but I probably estimated myself in a stronger position than I actually was.

Cutting on the side you don't want.
If I cut on the outside, can't black easily live? Or is that not the point, rather it will live small and isolated?

The point is that he will live in gote instead of sente. So you get a free move elsewhere.

Oh okay!
I definitely have to start valuing sente more. It's something I haven't had a lot of attention for so far, and probably something too important for SDK ranks to ignore.

Thank you!

Usually you have a choice in some local situation between e.g getting 20 points and sente or 30 points and gote (I use points loosely here, usually you can't count exactly so it's more like a position so-and-so or another different in some ways). Then you need to judge how valuable sente is which is hard (AlphaGo seems to be teaching us even top pros tended to undervalue it) and depends what other things there are to do on the board, but in this example if sente is worth more than 10 points (again hand-wavy) then better to choose the 20 points and sente option. However, with this cut example it's more like would you like 30 points and sente or 30 points and gote. Pretty obvious choice, if you think sente is negative you can always pass!

For the bottom invasion, it looks mostly like poor tactics. 116 at G2 misses the eye-stealing tesuji by one point. The wedge at 120 can be a tesuji in rare positions, but here you want to apply the principle "stay away from what you're attacking". After that it already looks difficult. 126 seems to miss the point entirely, I'd be concerned about the fact that your two stones at K4 only have two liberties. 130 also disregards liberties - that seems to be a common problem: the earlier N17 could be explained by the same kind of blindness.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

A couple of points nobody has mentioned. They are not to your question, but still important, I think.

(Or earlier.) Since you have made a big wall on the top side, you should take the opportunity to use it for attack. Pincer the Black stone on the right side. I like Q-07.

How about the descent to B-14, threatening both the Black group on the side and the top left corner? Maybe you cannot read out the corner, but your opponent probably can't either. And there is something there, at least White B-16, Black B-17, and maybe White B-18. Also B-14 aims at B-10, taking away a possible eye and threatening to connect to either side.

Edit: How about R-05 first?

White 116: The best play to take away Black's potential eye at or around J-03 is H-02. Possibly White should peep at H-03 first.

After Black lives on the bottom side:

White B-14 still threatens the Black corner, and threatens B-11

White can also kill the bottom left corner.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

From the fact that correct komi is around 7 pts. we can estimate that sente early in the game is worth around 14 pts. How big is that? Killing the bottom left corner would gain 14 pts. Killing the left side group after the fight on the bottom side would gain between 15 and 20 pts. or so. Killing the top left corner would gain quite a lot.

As a genera rule you do not want your opponent to invade and live with sente. That means that your moyo (Edit: or the part that he took, anyway ) actually belongs to him. He invades it, lives, and then plays somewhere else. (Edit: A free lunch!) One thing I did right as a DDK was if my opponent invaded and lived, I took sente. OC, my judgement sucked, but I had the right attitude.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.