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  Dominions Strategy & Tactics 

Very little is known about Dominions strategy and tactics, since the game has remained dormant for the first two decades after its invention. The game went online in the summer of 2002 with everyone (including the inventor) very much in the dark. Since then some strategical contours and some interesting tactics have emerged.

Extendable liberties
If a player seeks to keep his initial groups alive (gambits are possible), he should take care not to run out of extendable liberties too soon. An extendable liberty is one that points to a cell that is adjacent to at least one opponent's piece. A non-extendable or 'dead' liberty points to a cell that does not border on an opponent's piece. With one exception players may not extend from these, and although they count, they're useless for growing additional liberties, and vulnarable to suicide attacks.
The best pieces to create extendable liberties are compact 'fours' and 'fives'.

Let's say white opens with a five, and black replies with a five as indicated. Black now has two twin liberties - if white extends at A, black has C to further extend and if white moves at B (which is not an extension but the start of a new group) black can extend further at D. Likewise, if white moves at C or D, black can extend at A or B, cutting white in the process.
In most cases it will not be possible for an opponent to commit suicide at a twin liberty: if white moves a compact two at A, the piece remains white. On the other side white can commit suicide with a one (now commonly called a 'plug') at B. This would make his NW-liberty alive (extendable) and leave black with only one cell to extend, namely A. It would take at least a compact four to make a next twin liberty.
Plugs are precious, and white wouldn't spend one on a single piece. If black extends at B, he makes the white liberty at F alive, so white can wait. Let's assume he uses a compact four to make a new twin liberty at A, black follows suit at C and white invests a five to keep the group going and create a triplet liberty - we're in the right diagram.
If black wants to extend, he has only B and E. If he extends at B, white can keep up at F or, even better, close at E, so black is practically forced to extend at E (with a five if he wants to create at least a twin liberty, since the four is already on the board). Since white has placed a triplet liberty, he doesn't have to react immediately - there's still a twin liberty left! NOW white might consider a plug at B, depriving black of any possibility to grow his group at that end, while his own group can grow around the sacrificed plug.

Suicide attacks
I would advise against opening with a forked four because black can attack at the tail, leaving white with three dead liberties (ABC). In fact the forked four is doomed altogether. White can try to come to the 'rescue' with for instance a five at P, but he cannot connect at A because his liberties are dead. Black on his second move places a plug at B. It is crucial to make it a suicide because a black piece at B would give white two extension cells (AC). White has no better than a five at Q, and we're in the middle diagram.

Black proceeds with a five at C, and white, unable to play at A, has no better than to attack the attacker by extending from his right five. At this point, with the white group in atari (reduced to a single liberty), blacks best strategy is not to capture it. There's a simple reason: as long as it is white, black can employ it to move adjacent to it. The diagram on the right illustrates the capture resulting in twin liberties all around (EF-GH and a triplet at the bottom), yet it's not the best move. That would have been to extend at E and postpone the capture as long as possible (till one of the containing groups gets into atari itself, for instance) to employ the white pieces in case an opportunity arises.

This example is about the capture of a single piece (and the plug invested), but the reasoning holds for any group: dead liberties can be deadly!
It should be noted also that suicide resources are limited, but then, they're not limited to plugs alone. Compact and bent two's and even three's can quite often be employed.

Sections
A section is an isolated part of the beamstructure, disregarding color. In the example on the left white has opened with the six and black has played a plug. Like so much in this world, it's stupid but legal.

White cannot move adjacent to an opponent's piece and neither does he have to, because his group makes up a complete section. If black had played any piece but a plug, the resulting section would be bi-colored and thus contain more than one group, and white would be subject to the usual placement restrictions. If and only if a group (including a single piece of course) makes up a complete section, the player may freely extend from it: such a group has no dead liberties!

The middle diagram shows what might happen after players open with back to back disconnected five's. Both pieces make up a complete section and thus have no dead liberties. Next both white and black have extended with a six and both still may freely extend from any liberty of the resulting groups because both groups still make up a complete section.
In the diagram on the right white has put an end to black's freedom by adding to black's section, making it bi-colored. The section now consists of two groups from which neither player may extend freely: if black wants to extend he's restricted to ABC or D. White's group of two still makes up a complete section so a black move at A or B would make sense in that it extends from an existing group and simultaneously makes the white group subject to the usual restrictions.

Starting a new section is an important weapon that can be used to initiate a new local conflict. As a game proceeds, an increasing number of cells that are adjacent to only blank sides of the opponent appear. Placing a (preferably big) piece on such a cell presents the opponent with a problem: the piece has all its liberties (since it didn't invest one in a beam connection) and may be freely extended from! This usually is enough to trigger a local reply and thus initiate a new local conflict. Sooner or later, but often sooner, these local conflicts itself start to interact. Then it's beginning to look like Dominions (I mean, try to explain Go strategy in a world where no-one has ever played it :-) ).

Eyes
Two moves onwards from the last diagram, we can illustrate an eye.

Black has placed a further compact four - very questionable in strategic respect, but conveniently illustrative. White replies with a crossed four that creates a white eye at A. Only two pieces will fit at A and black has already used both! The crossed four and the top five - and also the groups formed by extending from them - live unconditionally.
A is not an eye for black: white still has a five to fit! If black does not extend at B, white might place a plug there to conveniently build around it, keeping the five in case the need for actual capture might arise. If white in the course of the game moves the five elsewhere (the need can easily arise), the eye at A has become absolute and all groups with a liberty at A live unconditionally, regardless of color.

Note that if black plays at B, white can extend at C, but more importantly: if black extends at B, white can connect at D, linking all groups to the eye, because the bottom white group still makes up a complete section!