Allah exists for He has made the world and brought it into existence, and who has done so must be existing.
SELF-EXISTENCE: Allah is self-existing in the sense that he does not depend on anyone for His existence. He is not a possibly existing being, for if He had not been self-existing, He like this world would have required someone to bring Him into existence, and that is not possible in the case of the Benefactor worthy of worship.
ETERNAL: Allah is eternal and has always existed in the sense that there was no time when He did not exist. He will always be existing in the sense that there will be no time when He will not exist. He is All-Powerful and has the power of willing and choos-ing in the sense that if He wills, He does a thing and if He does not will, He does not do it. This is evident for He made the world when He liked.
OMNIPOTENT: Allah the Almighty can do all that can be done and knows all that can be known, for all things are on the same level in relation to His Holy and Absolute Being. To say that He can do certain things and cannot do some others, or that He knows certain things, but does not know some others would mean giving preference to certain things to others without any co-gent reason, which is impossible.
OMNISCIENT: Allah is All-Knowing in the sense that everything is clear and manifest to Him and there is not anything hidden from Him, for Allah's all acts are perfect and thorough. Therefore, He is evidently All-Knowing.
ALL-PERCEIVING: Allah perceives everything, not with the help of any physical means, but in the sense that He knows everything that is perceived by senses, for Allah is free from having a body and its accessories. Allah Himself says: Eyesight does not perceive Him, but He perceives eyesight. He is Subtle and All-knowing. When Allah says that He is All-Hearing, All-Seeing, that means that He knows everything that is audible, but not through an ear and that He knows everything that is visible, but not through an eye.
EVER-LIVING: Allah is living
in the sense that it can be said about Him that He is able to do everything and that He knows everything, for it has been proved that He has power and know-ledge, and anyone who has power and knowledge is certainly living.
SPEAKER: Allah is Speaker, not in the sense that He speaks physically, but in the sense that He creates speech in some organism or body so that His message may be conveyed to His creatures. He has said: Allah spoke to Moses in a particular way. As Allah is Powerful, He is able to speak.
TRUTHFUL: Allah is Truthful in the sense that He tells actual truth, because every lie is abominable, and Allah is free from all that is ugly.
THE WILL OF ALLAH: Allah has a will in the sense that He does a thing as and when He deems it fit. He created a particular thing at a particular time in a particular form. He gives orders and that shows that He has a will.
AVERSION: Allah is averse in the sense that He prefers not to do a thing that He knows will cause evil. He did not create certain things at a particular time, although His Knowledge and Power are always on the same level. He has forbidden certain things. That shows His aversion.
source : http://www.islamicecenter.com/e-library/logic_islamic_rules/logic_islamic_rules_makarem_subhani_03.html