ASML intends to return cash to shareholders on a regular basis through share buybacks or capital repayment, subject to our liquidity requirements, current share price, market conditions and other relevant factors.

The following graph shows the last 5 years of Share Buyback repurchased, cumulative from initial start in 2006, in million EUR:
Below you find a link to the history table:
History Table

Previous share buyback programs under the 2016 Market Abuse Regulation (Nr. 596/2014):
2016-2017 program: link

2018-2019 share buyback program for up to EUR 2.5 billion
On January 17, 2018, ASML announced its new share buyback program to be executed in the 2018-2019 timeframe. ASML intends to purchase up to EUR 2.5 billion of shares which it intends to cancel upon repurchase, with the exception of up to 2.4 million shares which will be used to cover employee share plans.

The total amount of outstanding shares at the beginning of 2018 is approx. 427 million shares. Details on the share purchase can be found in the excel overview below: