Strategical Ideas

Passive Defense
The only defense possible albeit passive but enough to slow down or put end to opponent's attack.

Undermining the Centre

Placing the pieces in such a way that they co-ordinate, and undermine the opponents pieces which temporarily or completely control the centre.

Taking control of the Centre
Place pieces to control the Centre part of the board from where they influence many squares on the board. 

Threatening Moves
Advancing the pieces and marching towards opponents camp either with the hidden threat or without any immediate purpose but in the hope that they co-ordinate and wait for him to change the position of his pieces so the hidden nature of the threat flourishes itself.

Advancement of Castled King side pawn Cover
When to advance the king side pawn for an attack. Tests King safety. 

Defence from obvious weakness before your opponent has even begun to attack.

Pawn structure:
Attacking the opponents pawn to make it isolated, trading pieces to make it doubled. etc

Queens and rooks to the 7th
Placing the queen and Rook on the 7th or the 2nd rank.

Massing near the king for the attack
Arranging useful pieces necessary for king side attack.

Pawn storms
Or pawn chains, pawns wedge, pawn nail.

Destroying the castled king’s defenses 
Creating weak squares in opponents king side pawn cover.

Limiting the mobility of pieces.
Fixing up pawns to limit the mobility of pieces.

Which pieces to use to recapture. cxd5 or exd5 or Nxd5 etc etc

Avoiding En-passant/ doing en-passant.
Do enpassant only if you can weaken opponent's pawn structure, else not.

Blockade the passer pawns with one of your pieces.

Overprotection/Overworked Pieces:
protect the certain pieces further, especially the ones that control important squares/centre.

Pawn Break 
Advancing the pawn in attempt to break open the file. Especially in fortress structures the pawn break helps in activating the play. 

Offer of Simplification 
This was released. See STS 7.0. Placing Pieces in direction of trade.

Advancement of Queen Side Pawns or a/b/c pawns: 

Just like the advancement of f/g/h pawns but this is on the opposite wing. 

Fianchettoing the Bishop 

Keeps up the long diagonal and acts as a strong king's defense. 

Exchange of the Fianchetto Bishop 

Trying to find ways to exchange up the opponent's Fianchetto Bishop 

Knights to the 4th/5th Rank 

Advancing the knight to the 5th rank(Ng5, Nb5) pressures the pieces in opponent's camp. This is a threatening move that assists in king side attack, or intends to reposition itself to e4/d4 center where it will have access to many squares, or makes way for f-pawn advance.

That doesn't involve material gain. But just what it is - the pin. which forces the opponent to take the passive role and lose the mobility of his pieces by defending the pinned piece.

Pawn Race [Thanks, Jesper! for this] 
Advancing the pawns in late middle game transitions to endgame. 

King to the Centre
Bringing the King to the centre in the late middle game/early endgame. 

Late Castling either on the queen side or on king side as the form of defense in the Late openings/Early middlegame. 
Repositioning of the Pieces
When you find yourself in a situation where your attack grinds to a halt and that your opponent has defended well, your only resort is to reposition your pieces and attack again in a different way. 

Sacrificing a pawn for better activity
Sacrifice the pawn to obtain some compensation. 

Square Vacancy:
Occupying the vacant squares on enemies camp in order to create more pressure in adjacent areas.

Giving tempos either with a pawn or with pieces.

Simplification simply means to simplify the position by exchanging pieces when you're materially superior or positionally superior. Engines could find simplification easily, but I'd want to look for difficult simplification puzzles.

King Activity and King Safety:
When it's the right time to use king as the active piece. When not to castle, when to place the king in the corner.

Development and Piece Activity:
Activating the cramped pieces, and developing the pieces and posting them in good squares.

Positional Exchange Sacrifice
Giving up materially superior piece for positional reasons.

Bishop vs Knight
When to offer the Bishop for the trade with the knight and vice versa.

Offer of Simplification with pawns:
Advancing the pawns in the direction of trade/exchange.

and not exchanging up pieces when you're materially weaker, or you want to put up fight even if the position is about equal, Or you just want that piece for the later stage in the game and don't want to offer it up for an exchange because it's that good.