What is permissible
Bay (sale) is the foundation. A clean sale of a real asset for a real price, with both ownership and risk transferring, is the default permissible transaction. From bay, Islamic finance derives murabaha (cost-plus-markup sale) and salam (forward sale with upfront payment).
Ijara (leasing) is permissible. The lessor holds the asset and bears its risk; the lessee pays rent for use. Ijara wa Iqtina layers a binding promise to transfer ownership at the end of the lease, used in halal home and auto financing.
Partnership is permissible and preferred. Musharakah (equity partnership) and Mudarabah (profit-sharing partnership) align return with genuine risk. Diminishing Musharakah, used in halal mortgages, lets the homebuyer gradually buy out the financier.
What is prohibited
Riba is interest, broadly defined: any predetermined increase on a loan or in an exchange of similar commodities. The Quran addresses riba directly (2:275-280, 3:130, 4:161, 30:39) and prohibits it in absolute terms.
Gharar is excessive uncertainty in a contract. A contract where the price, quantity, or delivery of the subject is materially unknown is invalid. Conventional insurance and certain derivatives raise gharar concerns; takaful (cooperative insurance) is the structurally permissible alternative.
Maysir is gambling and excessive speculation. Pure-chance returns generated without productive activity are prohibited. Speculative leveraged trading, lottery instruments, and unbounded option speculation fall here.
The higher objectives
Beyond the technical permissibility of contracts, Islamic finance pursues the Maqasid al-Shariah: preserving faith, life, intellect, lineage, and wealth. A transaction can be technically clean and still fail if it harms one of these. This is why a Mufti's review of a product is not just a checklist; it is a judgment call about how the structure operates in practice.