My list of essential resources to study.

Mathematics of NL Hold'em video series on www.deucescracked.com by WiltOnTilt
The Eightfold Path to Poker Enlightenment series on www.deucescracked.com by Tommy Angelo
Book "Easy Game" By Andrew Seidman from www.balugawhale.com
Book "The Mental Game of Poker" by Jared Tendler from mentalgameofpoker.com
Bart Hanson's Podcast at www.seatopenpoker.net

Results Don't Matter

This is a very simple concept every good poker player knows but it’s very hard to grasp for average human being. We all too used to judge performance by results and we are all too result oriented in our life. But the fact is result of a single hand of poker does not matter. What matter is who made a mistake playing this hand? If you make (bigger) mistake then your opponent you lose money in the long run if he made mistake – you profit from it in the long run. 
To demonstrate this concept lets look at a very simple game. We make a deal to flip a coin. You put $1 on heads and I put $1.10 on tails. Assuming coin is not rigged and your probability of winning is 50% it does not matter which side the coin lands on every specific toss, this game is profitable for you in the long run. 
Same with poker. Poker is not a card game. Poker is the game of making deals. And if you make more profitable deals then your opponents than you make money in the long run. Cards in poker only used to bring variance in the game so players who make bad deals could win sometimes and that keeps them playing. 
Not being result oriented also helps your mental game. If you concentrate on making most profitable plays and don’t care about results of each single hand you won’t be affected by bad beats. Because you know if you got bad beat somebody had made very bad (and very profitable for you) deal with you. And you are happy about it.

Variance is my friend.

I love variance. Variance is the main reason that it’s much easier to make money at poker then at no variance game like chess for example. Variance is making sure that loosing players win sometimes and keep coming back to play again. Variance fueling delusional people’s beliefs that they are good at poker because they win sometimes and only bad luck doesn't allow them to win constantly. Seeing variance unknowledgeable people believe that poker is a game of luck, which is great because it gives them reason to not improve. Nobody needs skills in the game of luck.

When I embraced variance I realized that having more variance in a game is great for me. So now I’m trying to generate it when game is lacking it. For example in bad 2/5 tight passive game full of short stacks hand might play out this way:

MP (300) limps 5h5d
I fold Qd9c in HJ
CO (250) limps 7c8c
BTN limps, blinds complete. Pot $25. 
Flop Kd5c6h. Blinds check, MP checks to trap, CO checks, BTN checks.
Turn 9s. Blinds check, MP bets $15. CO calls to trap. All fold. Pot $55.
River 7d. MP checks scared of straight. CO bets $25, trying to get call from top pair. MP calls. Pot $105. Casino takes $10 rake (10%). Stack sizes now: MP $255, CO $345. Is this good for me? No, because now it’s $10 less for me to win at the table.

What if I try to introduce a bit more variance in this game?
MP (300) limps 5h5d
I raise Qd9c in HJ to $25
CO (250) calls 7c8c
BTN folds, blinds fold. MP calls. Pot $82. 
Flop Kd5c6h. MP checks to trap, I bet $35, CO calls, MP raises to 70, I fold, CO calls. Pot $232.
Turn 9s. MP bets 75, CO goes AI for 155, MP calls.
River 7d. Pot 542. CO wins with straight. Casino takes $15 rake (2.8%). MP reloads for 300. Stack sizes now: MP $300, CO $527. And I’m loving this. Yes, I just lost $60. But what do I get in return? 
1. There are $285 more at the table for me to win
2. MP is super tilted that he lost with flopped set. It’s very likely he’s now going to spew some more trying to get even.
3. CO is now full stack and he’s not used to play deep. He’s happy, orders another beer and will tend to chase his draws for any money, reinforced with positive result.
This outcome is great for me. Also I don’t really lose $60 here in the long run. Next time flop comes Kd2c6h and I take it down with cbet. So this is win-win situation.

Do I want to reduce variance in my results? Obviously, yes! But what’s not so obvious is how? I believe the only way to reduce variance is to increase your win rate by increasing your skills advantage over your opponents. Thinking of extreme example: if you have opponent who plays with his hole cards face up. It’s going to be pretty hard to lose in this game. Your win rate will be very big and variance is very low. (You still lose occasionally when you go all-in preflop with AA vs KK for example). So, to reduce variance I thrive to study poker off the table as much as possible. And it pays off in the long run.

Levels of poker thinking

There are different levels of thinking on which poker players can play.
For example:

Level 1 player thinks about his hand. All beginning players start on this level. Their thought process goes like this: “I have Tc2d, flop is Ts9s8s. I have top pair. Top pair is a good hand, so I’m not going to fold to all this crazy bets and raises”.

Level 2 player thinks about what hand his opponent have. For example: “I cbet two tone flop and got called. Now flush card comes on the turn. My opponent must have hit his flush so I’m not going to put any more money in the pot.”

Level 3 thinks about what his opponent think about his hand. “I raised preflop and cbet flop. Now Ace comes on the turn. If I bet my opponent will put me on AK so this is a good spot to bluff. ”

Level 4 thinks about what his opponent thinking about what he thinks about opponent’s hand. “Scare card comes on the turn and my opponent bets. This is a good spot for him to bluff so I should call him with my 3-rd pair.”

And so on… 

To exploit your opponent’s way of thinking you need to think on exactly one level above him. There is no point in being on level 3 and trying to bluff level 1 thinker – he’s just not going to fold his pair no matter how scary the board is.

Combinatorics

How many ways we can have AA in our hand? 
AcAs, AcAd, AcAh, AsAd, AsAh, AdAh – total 6 possible combinations.

How many ways we can have AK? – 16 (you can count yourself).

Now more interesting question: How many ways our opponent can have AA when we have Ad in our hand? 
AcAs, AcAh, AsAh – total of 3 possible combinations.
So when we were dealt an Ace chances that our opponent was dealt two Aces are less by 50% Our Ace blocks half of his combinations. We can say we have a ‘blocker’ to AA.

How to use this knowledge on practice?
Say our tight opponent open raises preflop from early position. We think he can have AA, KK, QQ, JJ, AK or AQ. When we look at our hand we see that we were dealt AK. Now we can deduce distribution of hands in our opponent’s range. He has 3 combos of AA, 3 of KK, 6 of QQ, 6 of JJ, 9 of AK and 12 of AQ for a total of 39 combinations. 
From here we know that he has: 
AA 3 out of 39 - 8%,
KK 3 out of 39 - 8%,
QQ, JJ, AK 21 out of 39 - 54%,
AQ 12 out of 39 – 30% of time.

Now let’s calculate our equity versus his range:
AK has 8% vs AA,
30% vs KK,
50% vs QQ, JJ and AK,
70% vs AQ.

For a total of 8 * 0.08 + 30 * 0.08 + 50 * 0.54 + 70 * 0.30 = 51% equity. 

So we should expect to win about half of the times we go all-in preflop versus this opponent.

Where does our edge come from?

There are 3 main ways to get advantage over your opponent in poker:
- skills
- cards
- position

More skilled player is going to win money from less skilled player over the long run.
If your hole cards better then your opponents you obviously have an advantage.
If you have position on your opponent you can see what he does before have to act and this gives you advantage on each betting street.

How to use this knowledge in game?
For example you are in BB with marginal hand. It’s folded to loose, aggressive player OTB who open raises. SB folded. Should you fold? You have positional disadvantage, but you think that large percentage of time LAG player will have cards weaker then yours, so you have cards advantage. So it boils down to skills. If BTN is a good player and you don’t have big skills advantage over him it’s better to fold. But if you think you much better then him, then it’s possible that you can make profit from playing your hand.
Another example is that sometimes you can find yourself in such a great game where your skills advantage over other players is so great that you can profitable play almost any two cards from late positions. Your skills and positional advantage allow you to overcome your cards disadvantage.

How to calculate if you have correct odds to call?

I will demonstrate it on this very simplified example:

2/5 No Limit Holdem
UTG tight, passive straightforward player opens to 20, 2 players call, you have As5s OTB. You call, blinds folded.
4 players to flop, pot $85. Flop Tc7s2d. Checked to you. You check.
Turn Ks, UTG bets $75. All fold to you. You think that UTG has top pair, good kicker and he’s not going to fold to your raise. Also it’s unlikely that he has set because he wouldn't open TT or worse pair UTG and he would cbet KK on the flop. So you should calculate if call is profitable. You need to call $75 to win $160. There are 46 unknown cards left in the deck. 9 of them are spades which will give you winning hand. Odds of spade coming on the river are 9 to 37 or 1 to 4. So to make call of $75 profitable you need to win over $75 * 4 = $300 when you make your flush. There is $160 already in the pot. So you need to make extra $300 - $160 = $140 on the river. This means that you can’t profitable call if UTG has less than $140 in his remaining stack or if you think it’s unlikely he will call your over $140 bet on the river when flush card comes. Also don’t forget that if you make just $140 on the river you will not have any profit – you will break even, to make profit you need to win more than that.