You can buy train tickets online through various websites, depending on your location and the train service you're interested in、Here are some popular ones:

In the United States:

1、Amtrak: [www.amtrak.com](http://www.amtrak.com) Official website for Amtrak, the US national passenger railroad service.
2、Trainline: [www.trainline.com](http://www.trainline.com) A popular platform to book train tickets across the US and Europe.

In the UK and Europe:

1、National Rail: [www.nationalrail.co.uk](http://www.nationalrail.co.uk) Official website for booking train tickets in the UK.
2、Trainline: [www.trainline.eu](http://www.trainline.eu) A popular platform to book train tickets across Europe.
3、Eurostar: [www.eurostar.com](http://www.eurostar.com) For booking train tickets between the UK and Europe.

In India:

1、Indian Railways: [www.irctc.co.in](http://www.irctc.co.in) Official website for booking train tickets in India.
2、RailYatri: [www.railyatri.in](http://www.railyatri.in) A popular platform to book train tickets and check train schedules in India.

In Australia:

1、NSW TrainLink: [www.nswtrainlink.info](http://www.nswtrainlink.info) For booking train tickets in New South Wales, Australia.
2、VIC Rail: [www.vic.gov.au/train](http://www.vic.gov.au/train) For booking train tickets in Victoria, Australia.
3、Trainline: [www.trainline.com.au](http://www.trainline.com.au) A platform to book train tickets across Australia.

Other countries:

1、China Railway Corporation: [www.chinarailway.com.cn](http://www.chinarailway.com.cn) For booking train tickets in China.
2、Japan Railway: [www.japanrailways.jp](http://www.japanrailways.jp) For booking train tickets in Japan.

Please note that some of these websites might have English language support, while others might be in the local language only、Additionally, some websites might require you to create an account or log in to book tickets.

If you're looking for a specific country's train ticket website, feel free to let me know, and I'll try to provide you with the relevant information!