Rules for the Base Game

Players control competing civilizations exploring space, discovering planets to conquer or settle, building an economy by consuming a planet's goods and building developments. The object of the game is to earn the most victory points from planets and developments played in their tableau, from consuming goods, and from bonuses from special developments.

There are five phases to choose from: explore, develop, settle, consume and produce. Players pick one phase per turn (two phases in a two-player game). Then everyone plays only the chosen phases in phase order. Players who chose that phase get an extra benefit. At the end of each round, players with more than 10 cards discard down to 10 and a new round begins.

The game continues until any player has 12 cards in their tableau, or when the VP pool is exhausted. At the end of that round points are added up. The player with the most points is the winner!

In case of a tie, the player with the most goods on the board plus cards in hand wins.

Cards may generally be played into your tableau by "paying" for them by discarding other cards. For instance, a planet of cost 3 (the large number) requires you to discard 3 cards to place it. (The smaller number next to it is the number of VPs you earn from having that card in your tableau.)

There are different types of planets:

Production: A colored circle indicates that this planet generates the corresponding good during the production phase.
Windfall: A white circle with a colored ring indicates that this planet generates a good immediately upon settling, but not during production.
Non-producing worlds: Gray worlds never produce goods.
Military: A red ring indicates that a planet cannot be settled by paying for it: instead, you need a sufficient military force (the red +X number present on some cards). No discards are needed in this case.

Summary of Phases

Explore = draw 2 cards; keep 1, discard the other
Develop = place and pay for a development
Settle = place and pay for a world, receiving any windfall good as indicated
Consume = use consume powers if possible, typically to discard goods for VPs. Note that once a consume power is activated, you must exhaust it (e.g. if you have 3 Novelty Goods, then if you trigger Consumer Markets to consume the first good, then the other two must also be consumed on Consumer Markets). 
          To consume a good in the BGA interface, click on the world with the good, and then click on the world with the consume power. 
Produce = place a good on each world without a good that produces one

Most cards indicate bonuses for certain phases; these are activated once they are in your tableau.

Phase Bonuses

These are the bonuses you gain for choosing each phase:
Explore = draw 5 additional cards OR draw 1 additional card and keep 1 additional card
Develop = discard 1 less card when paying for the development
Settle = draw 1 card after settling a world
Consume = Gain double victory points for consumed goods OR trigger a trade phase prior to Consume, which allows you to discard a good to draw cards equal to its trade value
Produce = Produce a good on one windfall world that does not already have a good

Note that in two-player games it is possible for one player to trigger both phase bonuses in Explore or Consume (e.g. in Explore, to draw 6 extra cards and keep 2), but the phase only happens once. It is not possible to trigger Produce twice. It is possible to trigger Develop or Settle twice, in which case the phase happens twice in a row.

Summary of Goods

Yellow = Alien Tech (trade value = 5)
Green = Genes (4)
Brown = Rare Elements (3)
Blue = Novelty Goods (2)

Expansion Rules: The Brink of War

Prestige

Gaining Prestige:

• Playing a card with a purple prestige symbol next to its point value provides 1 prestige to the owner when it is played.
• Various card powers provide prestige, typically as a result of taking another action, such as goods consumption. (Note: the Consume x2 action bonus does NOT double prestige gained using consume powers)

Prestige Leader: At the end of each phase, if one player has more total prestige than any other player, they take control of the Prestige Leader tile. The Prestige leader can also change hands immediately when a prestige leader spends prestige for an action, causing them to lose the lead. The prestige earned by the new leader in that phase and any subsequent phase while they remain prestige leader is counted as being on the tile.

At the start of each round, if the leader has prestige on the tile, they remove all the prestige from the tile (it remains part of their personal supply) and receive 1 VP chip and 1 card. If the prestige leader has no prestige on the tile (because they didn't earn any new prestige in the last round), then they receive only the 1 VP chip and no cards.

When there is a tie for the prestige leader, none of the tied players collect prestige on the tile, but all tied players will earn 1 VP chip at the start of the round.

Prestige at Game End Each prestige chip is worth 1 VP at game end. If a player has 15 or more prestige at the end of a round, the end of the game is triggered.

Prestige Search/Action Bonuses

Once per game, each player can use their prestige bonus card for either a search bonus OR an action bonus.

Search Bonus: A search bonus costs no prestige to use. Any player(s) declaring a search will get to execute the search action before any other phase is resolved in that round. The searching player first declares one of the 9 search categories. Then cards are revealed from the deck until a card matching the chosen category is found. The searching player can choose to take that card into their hand (ending the search action), or continue searching for a second matching card. If they continue to search for a second card, the second matching card must be taken, and the search ends.

Search Categories (Visual aid: https://boardgamegeek.com/image/693945/race-galaxy-brink-war)

Developments that provide +1 or +2 military (ignore temporary or specialized military)
Military Windfall worlds with 1 or 2 defense
Windfall worlds with 1 or 2 cost
Worlds (of any type) with a chromosome symbol (green X)
Windfall or Production worlds that produce Alien goods (ignore other alien cards)
Cards with Consume powers that consume 2 or more goods
Military worlds with 5 or more defense
6-cost Developments
Cards with settle takeover or defense powers (can only be chosen if takeover rules are on)

Prestige Action Bonus: A prestige action bonus costs 1 prestige to use. The player may then choose an enhanced bonus for their phase selection. (In a 2-player game, the player may select a second phase as normal)

Prestige Bonus Options

Explore: draw +13 (into hand), discard 11 (keep +2)
Explore: draw +9 (into hand), discard 6 (keep +3)
Develop: -3 cost 
Settle: -3 cost and +2 military, draw card after settling
Consume: Sell one good with +3 card draw AND 2x points for other goods consumed AND discard 0-2 cards for 1 VP each
Consume: 3x VP for all goods consumed
Produce: Draw 3, produce 2 windfall goods

New Worlds

Race for the Galaxy: New Worlds Promo is a set of 6 new start worlds. They can be added to any game (base game or expansions).

Star Nomad Raiders
Industrial Robots
Galactic Trade Emissaries
Terraforming Colonists
Abandoned Mine Squatters
Gateway Station

Image of the new start worlds: https://boardgamegeek.com/image/3884855