The rulebook is an early edition so some of the below may be
Wrong. Sorry. 

Buy in privates from phase two for 50-200%, or they close at phase
4. The Missisippi Bridge Company can be bought in phase one by the MP
or SSW - the two companies which start on the river - and no-one can
bridge the river until it is sold (or closed). The private auction is
"buy the first one or bid on a later one".

You can't buy more than 60% of a company, unless it's in the green or
brown zone of the stock market or during "price protection" (qv). You
can't sell so that more than 50% of a company is in the market. If you
sell a company you own more than 60% of you probably have to sell down
to 60%.

Down one for each share sold, except that if you are on the "ledge"
(just above the red zone on 18xx.games) a sale of a single share can't
push you under it. (A sale of two shares still pushes you down two
spots). Up one for being sold out (which includes "redeemed" shares
but not IPO). Right one for paying out in full, no movement for a half
pay, left one for no dividend.

(The rules say the "ledge" affects a left movement and that it doesn't
affect a right movement. This is just an unfortunate editing error;
it's the other way around, which is why there's up arrows just to the
left of the ledge for rightward movement.)

When shares are sold (either in a stock round or forced purchase) the
Director may "price protect" by buying the shares sold. They must buy
them all (and hence have sufficient cash on hand). The share price
does not then drop and play commences with the player to the left of
that Director. (If the selling player sold shares in more than one
company it is up to them what order shares are sold in.)

You are not required to account for possible price protection when
selling shares to get you under the cert limit - the example given is
selling one share of a company of which you hold four to get it into
the yellow zone of the stock market (where it doesn't count against
the cert limit), and the Director then price protecting. That's legal,
but on your next stock turn you'd still be over the cert limit.

There is scope for shenanigans with price protecting. If a Director is
the player on your right you can get multiple stock turns by dribbling
out their shares one at a time, with play passing back to you each
time (as, presumably, you steal some third party's company by buying
it all up).

You can, as a stock action, buy a private from another player at an
agreed-upon price.

As a stock action you can, on behalf of a company you run, redeem a
share from the market or a player. 60% of the company must remain with
players or the market. If the market has shares, you must redeem one
of those. If not, the player being redeemed from must consent. They
don't count as having sold it (they can buy that company later in the
stock round).

You can also reissue redeemed shares. These go back to the IPO at the
higher of the old par value or 75% of the market price rounded to the
nearest available par value. You can only do this if there are no
existing IPO shares. These shares, when sold, give incremental
capitalisation. You can't otherwise sell redeemed shares (eg in a
forced train purchase).

Note this means companies have both IPO and treasury shares and these
aren't the same. In particular, a player can't buy redeemed shares.

Full capitalisation (except incremental sales of reissued shares), 60%
to float (except the SLSF which floats at 20%). 

The number of ORs per SR increases from 1 to 3, 1825-style.

Lay two tiles or upgrade one. Upgrades are "reach some new track or
increase city value".

Large cities, dits, and offboards all count against your train's
capacity.

Unusually for a full-cap game, you get dividends from IPO or redeemed
shares.

You only are obliged to have a train if you have a route.

Each company has a destination hex. "Connection runs" are checked for
all companies (in share price order) after each company's turn. You
have a run if you could run from home to destination with a train you
own.

When you first find you have a connection run, your company does the
following: it takes a marker which is either placed on the destination
hex (where it doesn't act as a token) or taken as a bonus token for
ordinary use. The marker doubles the value of the destination city for
any train that terminates there.

(There is a variant where it _does_ act as a token and I'm not quite
clear on if 18xx.games implements that...)

You plan one set of train routes as if you were operating
normally. You must run a train from your home city to the destination,
but otherwise can you what you like. You either pay out (one right) or
withhold (no movement). Note this is a bonus set of routes and
payouts, completely separate from your normal actions this operating
round.

If the bank breaks the game ends at the next end of a set of operating
rounds. It ends immediately on player bankruptcy.