7.3  TECH COSTS   The cost in BPs of a TECH action is normally the square of the square of the new level, times the number of levels increased (so increasing a tech level from one to two costs 4 BPs, but increasing it from zero to two costs 8 BPs). Tech costs are paid from your TREASURY (not your current balance).

7.4  TECH TRADES   Technology may be traded between empires, via the TRADE and TAKE actions (see 7.5 and 7.6). Tech levels are not transferred directly: TAKE actions work the same way as TECH actions (the "taker" still has to pay for the new level) except that TAKE actions cost half as much as TECH actions.

7.5  TAKE   The TAKE action is used to spend BPs (from your treasury) on increasing a tech level by trade with another empire. You must specify the empire which is trading you this technology. This empire must have a tech level at least equal to the technology traded, and must specify a TRADE action (see 7.6) in the same turn. The cost of the action, if successful, is half the cost of the equivalent TECH action (see 7.3). Half this cost is paid into the treasury of the empire that offered the trade.
If you wish to take more than one tech level you must make more TAKE actions (and you've only got one per turn). The "multiple" option is not available.
TAKE   [ WHICH TECH ]  [ WHICH EMPIRE ]   [ NOT USED ]

7.6  TRADE   The TRADE action is used to trade technology to another empire, which may then take up that technology by using a TAKE action. You must specify the empire to which this technology is to be traded. This empire must have a tech level lower than the technology traded, and must specify a TAKE action in the same turn (see 7.5). You can trade a tech level the same turn as buying it outright, but you can't trade a tech level to someone else the same turn as buying it in a trade. There is no cost in BPs (and if the trade is successful then you may gain BPs).
As an option you may specify a tech level lower than your current tech level in the "number" box. In this case the empire taking the trade may only take technology up to the level indicated. The TRADE action takes one of the following formats:-
TRADE  [ WHICH TECH ]  [ WHICH EMPIRE ]   [ NOT USED ]  unlimited tech trade
TRADE  [ WHICH TECH ]  [ WHICH EMPIRE ]   [ LEVEL    ]   trade tech up to level

7.7  RESEARCH   Each turn (including the startup turn) you get one free tech level from research (after your actions are processed). The tech level you get is chosen by
chance in proportion to the tech levels you've already got.