Omnipotence is the attribute of maximal power ascribed to God in Jewish, Christian and Islamic theology. Its scriptural warrants are direct: "Is anything too hard for the LORD?" (Genesis 18:14); "with God all things are possible" (Matthew 19:26); and the Qur'an's frequently repeated formula that God has power over all things (2:20 and often). The Latin creeds open by confessing God the Father omnipotentem, rendering the Greek pantokrator, though the Greek means ruler of all rather than able to do all, and the shift of sense between them is often noted.
The philosophical difficulty is what "all things" is supposed to cover. The standard scholastic answer, given by Aquinas in Summa Theologiae I.25, is that omnipotence extends to whatever is absolutely possible, and that a self-contradiction does not describe a thing that might be done but is merely a form of words that has failed to describe anything; God's not making a square circle is therefore no limitation. A minority position associated with Descartes held that God's power extends even to the necessary truths, which God freely established and could have established otherwise. A third question is whether God can act contrary to God's own nature, lie, sin, cease to exist, and the usual answer is that these are not powers at all but incapacities belonging to perfection.
The paradox of the stone, whether God can make a stone too heavy for God to lift, is the schoolroom form of the problem, and the standard reply is that the description is incoherent rather than that it names something beyond God's power. Islamic kalam took a more radical route on a neighbouring question. Ash'ari occasionalism denied secondary causation altogether: God creates each event directly, fire does not burn but God creates burning at the moment of contact, and what we call laws are habits of divine action. Al-Ghazali argued this in the Incoherence of the Philosophers, partly to secure the possibility of miracle; Ibn Rushd replied that it destroys the intelligibility of the world and with it the possibility of knowledge.
In modern theology omnipotence is more often qualified than denied. Process theology, following Whitehead and Charles Hartshorne, holds that God persuades rather than coerces and has no unilateral power over events. Kenotic theologies hold that God has freely limited the exercise of power to make room for creaturely freedom. Both are advanced largely in response to the problem of evil, and both are criticised, by classical theists and by atheists alike, for surrendering what the traditions have meant by God in order to defend it.