Allahu Akbar ― A short study of its meanings

بسم الله الرحمن الرحيم

Allāhu akbar is often translated as ‘Allāh is the greatest.’ This translation may not be entirely accurate. Perhaps a more accurate translation is ‘Allāh is greater.’
The takbīr (Allāhu akbar) is composed of two words: (The Sanctified Name) Allāh and akbar.
Ism tafdīl
The word akbar is an ism tafdīl.
Ism tafdīl as a concept exists in the English language. In English, adjectives (a word that describes a noun) can be structured to be either comparative or superlative. 
Comparatives and superlatives are special forms of adjectives that are used to compare more than one noun (object/thing). For example, for the adjective smart, the comparative is smarter, and the superlative is smartest. 
Comparative adjectives mean more. They commonly end in -er. Examples include bigger, faster and stronger.
Superlatives mean utmost. They commonly end in -est. Examples include biggest, fastest and strongest.
In Arabic, both comparative and superlative are termed ism tafdīl.
Akbar is an ism tafdīl
Akbar linguistically comes from the trilateral root kāf―bā―rā which denotes a meaning of greatness. This corresponds with one of Allāh’s Names Al-Kabīr.
Since the word akbar is an ism tafdīl it can be translated as greater or greatest depending on its word structure and context. The word akbar in the takbīr (Allāhu akbar), however, takes the comparative meaning which means ‘greater.’ 
Allāhu akbar is thus translated as ‘Allāh is greater.’
The takbīr is open-ended
The phrase ‘Allāh is greater’ is an incomplete sentence. It begs the question, “Greater than what? What is Allāh greater than?” 
The object which Allāh is greater than is omitted and therefore the takbīr is left open-ended. 
The open-endedness (or incompleteness) of this phrase is made complete by context. For example, when the caller to prayer (mu’adhdhin) is heard saying, “Allāhu akbar! Allāhu akbar!” the one who is engaged in business and trade immediately remembers and acknowledges that Allāh is greater than his business and trade, and therefore returns to his Lord answering the call to prayer by establishing the prayer for His remembrance. Similarly, the one who is engaged in a social activity immediately remembers and acknowledges that Allāh is greater than his social activity (and social peers), and therefore returns to his Lord answering the call to prayer by establishing the prayer for His remembrance. He goes from the lesser to the greater.
A more common example is the takbīr that occurs in salāh. The takbīrāt (pl. of takbīr) give meaning and life to the strict rulings governing the prayer. In the prayer, one is not allowed to say anything other than the Words and Praises of Allāh because Allāhu akbar (i.e. the Speech of Allāh is greater than the speech of others). In the prayer, one is not allowed to turn his body away from his Lord because Allāhu akbar (i.e. Allāh is greater than any other thing that is turned to). 
Consequently, the first takbīr is called takbīratul-ihrām (the takbīr of inviolability or prohibition). In other words—subsequent of this takbīr—that which was permissible like eating and drinking becomes prohibited during the prayer because Allāhu akbar (i.e. Allāh is greater than all of that, and therefore focus all attention and efforts on Him). 
The takbīr is legislated in almost every movement of the prayer. It partially serves as a means by which to draw oneself out of heedlessness as it is plausible for the mind to dwell in other matters during the prayer. The believer is taken from the remembrance of the lesser to the remembrance of the greater.
Takbīr and Al-Kabīr
Al-Kabīr (The Most Great) is one of Allāh’s Names. The takbīr originates from this Name. It is a Name, when truly understood, brings tranquillity and confidence to every person who is overwhelmed. It is a Name that reminds us of our priorities, of where true greatness lies, and who is ultimately in control.
This Name connotes many subtle meanings and attributes—all included in what is termed greatness—like Al-Haq (The Truth), Al-A'alā (The Most High), Al-Ghaniyy (The Rich and Self-Sufficient), Al-‘Azīz (The Mighty), Al-Qadīr (The Most Able), Al-Ajall (The Most Exalted, Noble and Beautiful), Al-A‘alam (The Most Knowledgeable), Al-Ahkam (The Most Wise), et al.
People incline and are drawn to these qualities, and thus the takbīr serves to affirm them wholly and perfectly for Allāh alone. The takbīr is heard and said in the adhān and salāh because many people neglect the prayer in an attempt to acquire these attributes. 
So if a person seeks provision and riches then he should recognise that Al-Kabīr is Al-Ghaniyy and with Him are the riches that he seeks, if he seeks 'izzah (honour) or he fears what others may do to him then he should recognise that Al-Kabīr is Al-Qadīr Al-‘Azīz and that He alone is his supreme guardian. 

The Prophet sallallāhu 'alayhi wa sallam would hasten to the prayer when difficulties arose, seeking counsel and refuge through His Attributes of Greatness.
Implications of the takbīr
Allāhu akbar is the provision of the believer through which he seeks strength, courage and hope; it expels fear and anxiety from his heart. This is perhaps why the mujāhidīn when engaging the enemy say the takbīr—for the enemy with all its artillery, wealth and numbers, in spite of it all, the mujāhidīn know there is a guardian greater than them and the power they have amassed. 
Perhaps this is why the Prophet sallallāhu 'alayhi wa sallam said, “Allāhu akbar! May Khaybar be destroyed!” [Ahmad]
Allāhu akbar is the instrument of the believer through which he seeks difficulties to be lightened and made easy. Allāh said, “And seek assistance with patience and ṣalāh, and truly it is extremely heavy and hard except for al-khāshi’īn (those who are fearful and in awe of Him).” [2:45]
Khushū’u is achieved through the takbīr; acknowledging with certainty and an active heart and a conscious mind that Allāh is akbar than every other thing.
Allāhu akbar is the tool of the believer through which he purifies his ēmān (faith) in Allāh. By way of the takbīr he affirms the Name Al-Kabīr, recognising that utmost greatness is for Allāh alone, which in turn removes from his heart and mind unbefitting assumptions of Him including shirk. That is because Allāh is greater than needing any assistance or partner. 
By way of the takbīr he affirms Absolute Greatness for Allāh in His Essence, Names, Attributes and Actions ― a Greatness free from any shortcoming, deficiency and blasphemy; a Greatness that is unique and specific to Him alone. 
Because of the takbīr, there is lā ilāha illā-Allāh, subhānAllāh, alhamdulillāh et al.  Because of Allāhu akbar He declared His greatness, saying:

“And to Him belong the most beautiful Names.” [7:180]
“Do you know any similar to Him?” [19:65]
“There is nothing like Him.” [42:11]
والحمد لله رب العالمين
وصلى الله وسلم على نبينا محمد

Abu Unays