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I was just wondering if someone could explain the difference between istislah and qiyas to me and perhaps provide some examples for me. They both seem to involve the use of deductive reasoning and the use of ones' ijtihad and I just wanted to clarify any misconceptions I may have.

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Both are well explained on wikipedia, especially qiyas:

Istislah (Arabic استصلاح "to deem proper") is a method employed by Muslim jurists to solve problems that find no clear answer in sacred religious texts. It is related to the term مصلحة Maslaha, or "public interest". (wikipedia)

Note that Istislah is only applied if there's no text or a deduced analogy based on a text, so Istislah applies only after checking these two points.

Some scholars also call Istislah: al-Masalih al-Mursalah المصالح المرسلة: These are interests, which the texts of shari'a neither explicitly allowed nor forbade.
Some people relate this method to the Maliki school of fiqh only, but even scholars of other schools admit that they use it like the Shafi'is and Hanbali's with differences, for example Istislah is not used for the deduction of rules in worship matters. (In his doctor thesis of Sheikh al-Buty (May Allah have mercy with him) showed by examples that even those scholars who criticized the Maliki school for using Maslaha and Istislah used it, but the major difference was in the definition of the term).

Maslaha or maslahah (Arabic: مصلحة‎‎, "public interest") is a concept in traditional Islamic law. Maslaha is not Shari'a, but it is a concept that belongs to Islamic jurisprudence (also known as fiqh). It is one of the secondary sources in Islamic jurisprudence used by some "madhhab" to interpret Shari'a ... in order to set rules. It is invoked to prohibit or allow something on the basis of whether or not it serves the common good or public welfare. (wikipedia)

The Masalih (points of interest) are classified as follows:

  • necessary: Those are all the points of interest to save either the life, the mind, the money (possession), the religion/faith, the honor, the lineage.
  • wanted: Those are all the points of interest that make life easier or would create a bigger harm without fear for the necessary points of interest.
  • improving: Those are anything that makes life beautiful, such us things that would gentle the morals, and improve the transactions and image.

Examples on Istislah or Maslaha

  • One major example for Maslha: Is the collection and compilation of the qur'an in one mushaf (book), as it neither is prescribed by qur'an nor sunnah, but was a point of major public interest to keep and save this religion.

  • An other example which shows the importance of Maslaha is that the sahaba () agreed or had consensus in the punishment for drinking wine as described in Muwatta' Malik:

    Yahya related to me from Malik from Thawr ibn Zayd ad-Dili that Umar ibn al-Khattab asked advice about a man drinking wine. Ali ibn Abi Talib said to him, "We think that you flog him for it with eighty lashes. Because when he drinks, he becomes intoxicated, and when he becomes intoxicated, he talks confusedly, and when he talks confusedly, he lies." (80 lashes is the same amount as for slandering) Umar gave eighty lashes for drinking wine. (See Book of drinks 42)

  • Allowing to hit a condemned person under some condition. Note that generally it is not allowed to hit a person, but in cases of a public interest scholars have defined and created rules to allow or forbid the use of such a act without abuse!

  • Allowing the wife of somebody who has been absent or missing without any trace for 4 years to get married as this is a prior interest of the wife as she needs somebody who is in charge for her etc.

  • An important Maslaha of these days is writing down marriage contracts and marriage registration. which are often needed to testify whether spouses with different names in non-Muslim societies are really married!

Please note that Istislah isn't that far from Istihsan:

Istihsan (استحسان) is an Arabic term for juristic "preference". In its literal sense it means "to consider something good". Muslim scholars may use it to express their preference for particular judgements in Islamic law over other possibilities. It is one of the principles of legal thought underlying personal interpretation or ijtihad. (wikipedia)

Imam a-Shahatiby even confirmed that both might be considered as the same, but there was a difference in the definition which considers Istihsan as a special case, whil Istislah is general.

Qiyās (Arabic: قياس‎‎) is the process of deductive analogy in which the teachings of the Hadith are compared and contrasted with those of the Qur'an, in order to apply a known injunction (nass) to a new circumstance and create a new injunction. Here the ruling of the Sunnah and the Qur'an may be used as a means to solve or provide a response to a new problem that may arise. This, however, is only the case providing that the set precedent or paradigm and the new problem that has come about will share operative causes (عِلّة, ʿillah). The ʿillah is the specific set of circumstances that trigger a certain law into action.

An example of the use of qiyās is the case of the ban on selling or buying of goods after the last call for Friday prayers until the end of the prayer stated in the Quran (62:9).
By analogy this prohibition is extended to other transactions and activities such as agricultural work and administration. (wikipedia)

Other examples of the use of qiyas

  • The analogy between male slave and female slave in punishment for adultery based on quran

    ... But once they are sheltered in marriage, if they should commit adultery, then for them is half the punishment for free [unmarried] women. ...

  • Qiyas of paying the price of zakat al-fitr instead of foodstuff as described in the hadith.

  • The analogy of somebody who eats and drinks intentionally in Ramadan to a person who had intercourse in Ramadan when it comes to the kafara (at least for the Hanafi and Maliki school).

I hope i could make somethings clear!

An other Source.

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Istislah is to consider whatever is best for the common good of society.

Example: In Morocco, a girl was forced to marry the man who molested her. The judge used the idea of Istislah as an excuse for it as the man had done sexual things to her. (Maliki example)

Qiyas is to take a legislated ruling that is specific to a matter and make it general; as in comparing two similar things and giving it the same ruling.

Example: Eating donkey meat is forbidden. A horse is similar to a donkey, therefore, horse meat is also forbidden. (Hanafi example).

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