Answered by Shaykh Hamza Karamali, SunniPath Academy Teacher
What is the difference between usool al fiqh and al Qawaai’d al Fiqhiyyah?
In the Name of Allah, Most Merciful and Compassionate
The discipline of legal methodology (usul al-fiqh) teaches us how to derive legal rulings from the primary sources of Islamic Law, such as the Quran and the prophetic sunna. It teaches us how to read the primary sources in an honest and unbiased manner to figure out what Allah Most High really wants from us.
The discipline of legal maxims (qawa`id fiqhiyya) teaches us the underlying structure and patterns of the rulings that have been derived from the primary sources. A famous example of such a maxim is, "Certainty is not lifted by doubt." Another example is, "Something obligatory is not left except for something else that is obligatory."
These maxims are madhab-specific and are used by scholars to extrapolate existing rulings of Islamic law to apply to new cases. This extrapolation is a complex procedure that often involves the interplay of many different maxims. The mark of a mufti is his/her mastery of this discipline. 
A Common Mistake
Islamic Law has hundreds of maxims and applying them to new situations requires sound knowledge, deep insight, and rigorous training at the hands of experts. A common mistake in our times is to reduce these maxims to the five most universal ones, or to the five universal purposes (maqasid) of Islamic Law, and to then use these limited number of maxims to derive rulings for new circumstances or, even worse, to invalidate rulings that have been established by primary texts.
It is extremely important to understand that legal maxims are inductively derived from existing rulings that have been explicitly derived from the primary sources. This means that if all applicable maxims (not just one or two) are taken into consideration, then the existing rulings can be extended to new circumstances. However, a number of contemporary scholars (including Shaykh Muhammad Sa`id Ramadan al-Buti) point out that it is logically inconsistent to use these inductively derived maxims to invalidate the very rulings that they have been inductively derived from.  In other words, rulings that have been derived using the primary sources cannot be "undone" using legal maxims.
And Allah Most High knows best.
 Shaykh `Abdullah al-Lahji (Allah have mercy on him)--a famous Shafi`i scholar of this century--explained that the benefit of studying the the discipline of legal maxims is, "(1) To easily discover the the rulings of new situations that are not discussed in an explicit text. (2) To learn disparate legal rulings in the shortest possible amount of time ..." (Idah al-qawa`id al-fiqhiyya li tullab al-madrasa al-sawlatiyya, p. 7)
 Shaykh `Abdullah al-Lahji (Allah have mercy on him) defined the discipline of legal maxims as, "Rules through which the rulings of new situations are known when there is no explicit text from the Quran or sunna that addresses them." (Idah al-qawa`id al-fiqhiyya li tullab al-madrasa al-sawlatiyya, p. 7)
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