Holding one entry for three traditions makes this question unavoidable, so it is put here rather than buried. It does not have an agreed answer, and it is really two questions: whether the three traditions refer to the same being, and whether they describe that being compatibly. Almost nobody in the debate denies that the descriptions differ. The argument is over whether a difference of description defeats sameness of reference.
Catholic teaching answers yes for Islam, and does so at the level of a council. Nostra Aetate (1965) says of Muslims that "they adore the one God, living and subsisting in Himself; merciful and all-powerful, the Creator of heaven and earth"; the Catechism, quoting Lumen Gentium, says that they "together with us adore the one, merciful God". The relation to Judaism is not in question in the same way, since the church holds the Hebrew scriptures as its own. Not all Christians accept the conciliar position, and several evangelical and Reformed bodies reject it explicitly.
Jewish authorities have split along a line running opposite to the Christian one. Maimonides ruled that Muslims are not idolaters, their monotheism is unqualified, while classing Christian worship as avodah zarah, foreign worship; the passages saying so were cut from many printed editions by Christian censors. Against that, Tosafot held that gentiles are not warned against shittuf, associating another with God, and later Ashkenazi authorities used the category to treat Christian worship as permitted to Christians though not to Jews. Menachem Meiri went further and exempted the "nations bound by the ways of religion" from the laws of idolatry altogether. None of these positions was universally accepted and the disagreement is live.
The Qur'an contains both moves. 29:46 instructs Muslims to say to the People of the Book: "our God and your God is one, and unto Him we submit". 5:73 says that those who call God the third of three have disbelieved. Muslim readers have reconciled these differently, and the reconciliations track the exegetical split described in the previous section.
Modern philosophy of religion puts it as a question about reference. The volume edited by Miroslav Volf out of the Yale consultations collects Christian, Jewish and Muslim contributors arguing largely that reference can hold across serious doctrinal disagreement, on the model that two people can be talking about the same person while believing incompatible things about him. Others argue that a description can be wrong in ways that make it fail to pick anything out, and that the Trinity, or its denial, is a difference of that kind. The dispute is not academic: when Wheaton College placed Larycia Hawkins on leave in December 2015 for writing that Christians and Muslims worship the same God, and opened proceedings that ended in February 2016 with her departure, this was the question at issue, in public.
This entry does not settle it, and the single row it occupies should not be read as settling it either. What can be said without controversy is narrower and worth stating plainly: the three traditions share a genealogy, a large part of a scriptural cast, and the claim that there is exactly one God. Whether that is enough to make the object of worship one thing is a theological judgement, and an encyclopedia has no standing to make it.