〜ことができる
can, be able to (formal)
Verb dictionary form + ことができる
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Dictionary form + ことができる is another way to say "can": ピアノを弾くことができます, "I can play the piano". こと turns the verb into a noun, and できる does the rest, just as in 日本語ができる.
It means the same as the potential form but sounds more formal and deliberate, so it's common in writing, rules and instructions: このカードで電車に乗ることができます, "you can ride trains with this card".
It also covers what's allowed or possible, not just ability: ここでは写真を撮ることはできません, "you can't take photos here". Adding は makes the "no" sound firmer.
Don't confuse it with ことがある (experience, "have done"), which differs by one word.
Examples
私はピアノを弾くことができます。
I can play the piano.
このカードで電車に乗ることができます。
You can ride the trains with this card.
ここでは写真を撮ることはできません。
You can't take photos here.
一人で着物を着ることができません。
I can't put on a kimono by myself.
図書館では本を三冊まで借りることができます。
At the library you can borrow up to three books.