Is it lawful to buy and sell dogs?

The opinion of the majority of jurists
The majority of jurists have maintained that selling dogs is impermissible. They based their opinion on the hadith reported by Abu Mas'ud al-Ansari (may God be pleased with him) who narrated that the Messenger of God (peace and blessings be upon him and his family) prohibited receiving payment for the sale of dogs and the earnings of a prostitute and soothsayer. Jurists stated that from among the conditions of a sale contract is that the sold item must be pure; there is a scholarly agreement on the impure nature of dogs.

To facilitate the matter, in Islamic law, owning or exchanging a dog for any lawful purpose must not be through a transaction involving a sale and purchase but through relinquishing control of it i.e. the person who owns the dog relinquishes control of it to someone else in return for a monetary compensation. In this case, the money is not considered a price for the dog but for its relinquishment.

This is not a sham deal; it is different from a sale in that as soon as the person who relinquishes control of an article receives the money, he is not obliged to guarantee the relinquished article or even its deliverability. On the other hand, in a sale, the seller continues to guarantee the sold article until the buyer takes possession of it.
The luminary Shafi’i scholar, al-Qalyubi, wrote in his meta-commentary on Sharh Al-Jalal Al-Muhalla (2/383), “It is valid to agree on a benefit such as that derived from a dog or dung; the money exchanged is in return for relinquishing control of the article and not in return for the derived benefit or the article’s possession.”

The opinion of Hanafi jurists and others
The Hanafi jurists and others who maintained the same opinion have permitted selling dogs which are kept for lawful purposes such as hunting, guarding, etc. They based their opinion on the hadith reported by Jabir Ibn Abduallah (may God be pleased with them both) in which he said, "The Messenger of God (peace and blessings be upon him) prohibited receiving payment for selling dogs except for those kept for hunting" (recorded by al-Nisa`i). Therefore, there is problem in trading in or selling dogs for lawful purposes.

The ruling
It is lawful and there is no objection in Islamic law to trading in dogs kept for hunting or any other lawful purposes such as those mentioned above. This permissibility is based on the opinion of Imam Abu Hanifah or on paying money in return for relinquishing control of a dog according to the opinion maintained by the majority of scholars.
And God Almighty knows best.