1. 建立;创立;设立；制定
    If someone establishes something such as an organization, a type of activity, or a set of rules, they create it or introduce it in such a way that it is likely to last for a long time.

    e.g. The UN has established detailed criteria for who should be allowed to vote...
           联合国已经制定了有关投票资格的标准细则。
    e.g. The School was established in 1989 by an Italian professor.
           这所学院由一名意大利教授于1989年创建。

2. 建立，开始（联系）
    If you establish contact with someone, you start to have contact with them. You can also say that two people, groups, or countries establish contact.

    e.g. We had already established contact with the museum...
           我们已经和那家博物馆建立了联系。
    e.g. Singapore and South Africa have established diplomatic relations.
           新加坡和南非已经建立了外交关系。

3. 确定;查实;证实
    If you establish that something is true, you discover facts that show that it is definitely true.

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    e.g. Medical tests established that she was not their own child...
           医学化验证实她不是他们的亲骨肉。
    e.g. It will be essential to establish how the money is being spent...
           查清楚这笔钱将作何用途至关重要。

4. 使立足;使被认可;确立(地位)
    If you establish yourself, your reputation, or a good quality that you have, you succeed in doing something, and achieve respect or a secure position as a result of this.

    e.g. This is going to be the show where up-and-coming comedians will establish themselves...
           这将是大有前途的喜剧演员们让自己获得认可的节目。
    e.g. He has established himself as a pivotal figure in US politics...
           他已经确立了自己在美国政界的核心地位。