Short Answer 
The motives of groups like Al-Qaeda and ISIS can be understood through three steps: their fundamentalist beliefs in a strict interpretation of Islam, their shared goal of establishing a religious government or caliphate, and the misconceptions surrounding their true objectives, which primarily focus on enforcing their radical interpretations through violence rather than promoting tolerance or liberation.
Step 1: Fundamental Beliefs
The foundation of groups like Al-Qaeda and ISIS lies in their fundamentalist beliefs. These beliefs are rooted in a strict interpretation of Islam that advocates for the implementation of Islamic law in all spheres of life. This perspective frames their worldview and justifies their militant activities, pushing them toward their larger objectives.
Step 2: Establishing a Religious Government
These groups share a common motive to create a government based on their religious ideology. Specifically, they aim to establish a caliphate, which is a political and religious entity governed by Islamic principles. The desire to impose Islamic governance affects their operational strategies and often escalates to violent campaigns against those who do not share their vision.
Step 3: Misconceptions About Their Goals
It’s essential to recognize that the narratives surrounding these groups often include motives like liberating Muslim women or promoting tolerance. However, such views do not reflect their primary objectives. The consistent focus of Al-Qaeda and ISIS is on creating a religiously governed state that aligns strictly with their radical interpretations, often leading to extremism and violence against dissenters.