This is just a basic glossary. If you want a more detailed glossary of Islamic financial terms, Harvard University's Islamic Finance Project DataBank has a comprehensive glossary. The Meezan Bank glossary is quite comprehensive as well.
Amana: A transaction in which one party holds the property of another in a safekeeping trust.
Batil': Invalid (as in a contract or transaction).
Bay': Trade or commercial activity.
Bay'-bithaman-'ajil: Deferred payment sale. Customer approaches a bank and requests that the bank purchase an item for the customer. The bank purchases the item and sells it to the customer at an agreed-upon markup in installments. Same as murabaha.
Bay' al-dayn: Lit. trading of debt. The Shari'ah-compliance of debt transactions is disputed. More conservative scholars oppose bay' al-dayn at anything but par value because what is being sold is debt (i.e. money owed) and therefore any difference between par value and trade value would be riba. Other scholars disagree and believe that the trade of debt is permissible as long as the debt represents installment payments on an asset owned by the debt-holder. Under this interpretation, the debt sale is actually the sale of the creditor's share in the asset being purchased in the underlying transaction and therefore purchase at a value different from the par value represents an appreciation of the spot price of the underlying asset.
Bay' al-'ina: One party sells an asset to another on credit and then buys back at a discount.
Bay' al-kali' bi-al-kali': Sale of one debt for another; almost all scholars agree this is haram.
Bay' muajjal: A sale in which the seller buys goods for the buyer, who pays an agreed amount in full at some future date or in installment payments between the sale date and a future date.
Bay' salam: A sale with advance payment for future delivery.
Bay' al-urbun: Purchase with initial good faith payment that is applied to purchase if buyer makes purchase and is non-refundable if he does not.
Fatwa: pl. Fatawa: Legal pronouncements issued by an expert in Islamic jurisprudence (fiqh).
Gharar: An element of a transaction that is indeterminate and, therefore, makes the transaction void (batil).
Ijara: Lease contract; often long-term.
Ijara-wa-iqtina: Lease contract with a purchase option upon expiration; often long-term.
Ijma: Jurisprudential ruling by consensus.
Istisna'a: A variation of murabaha that permits goods to be financed while still under construction or manufacture
Maysir: Gambling; any activity where producing an unearned profit determined by chance.
Mudaraba: Partnership where profits are shared in agreed proportion and loss is borne by the financier according to his share.
Mudarib: In mudaraba, he is the manager (entrepreneur).
Murabaha: Cost-plus-profit contract.
Musharaka: Partnership where profits are shared according to a pre-arranged ratio. Losses are borne according to capital contribution.
Musharaka mutanaqisah (diminishing Musharaka): Finance company and the buyer have joint ownership of a house. Over time, the buyer pays the finance company a share of the market rent corresponding to its ownership share and the remaining portion of the monthly payment buys out the finance company's ownership share in the house over time. The partnership ends when the buyer owns the house outright.
Qard hasan: Interest-free loan. The borrower may pay a hiba (gift) at repayment as a sign of appreciation to the creditor.
Rabb-ul-mal: In mudarabah, he is the capital contributor.
Riba: Unlawful gain by way of excess or deferment. Most scholars include interest in this category.
Sarf: Currency exchange.
Sukuk: An asset-based investment represented by a "Participation Certificate" similar to a bond where the profit or loss of the underlying asset is shared between the holders of the security in a pre-arranged ratio.
Tawarruq: lit. monetization. A transaction in which a commodity is sold by the lender to the borrower with payment in installments and the commodity is then sold on the spot market.