LLP, Limited Liability Partnership: a partnership where a partner's liability for the debts of the partnership is limited except in the case of liability for acts of professional negligence or malpractice. In some states, LLPs may only be formed for purposes of practicing a licensed profession, typically attorneys, accountants and architects. This is often the only form of limited partnership allowed for law firms (as opposed to general partnerships).
A series LLC is a form of limited liability company that provides liability protection to multiple "series". Essentially, it's a master LLC with separate divisions, each protected and operating independently. As an entity, the series LLC is geared towards businesses where investors own multiple companies, with each series being protected from the debts and obligations of the other series. Currently, only several states support this option, including Delaware, Illinois, Iowa, Nevada, Oklahoma, Puerto Rico, Tennessee, Texas, and Utah.
A business entity is an entity that is formed and administered as per corporate law in order to engage in business activities, charitable work, or other activities allowable. Most often, business entities are formed to sell a product or a service. There are many types of business entities defined in the legal systems of various countries. These include corporations, cooperatives, partnerships, sole traders, limited liability companies and other specifically permitted and labelled types of entities. The specific rules vary by country and by state or province. Some of these types are listed below, by country. For guidance, approximate equivalents in the company law of English-speaking countries are given in most cases, for example: