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should the Market Capitalization be equal to the Equity of the firm
Lots of questions: In general, no. Market Capitalization and Equity represent 2 different things.  Equity first, the equity of a firm is the value of the assets (what it owns) less its liabilities (what it owes) and consists (broadly) of two components - share capital (what the firm gets when it sells to investors as part of an IPO or subsequent share issue) and retained earnings (what the firm has as a result of making profits and not paying them out as dividends). This is the theoretical liquidation value of the firm - what it is worth if it stops trading, sells all its assets and pays all its debts. Market Capitalization is the current value of the future cash flow of the firm as perceived by the market - the value today of all the dividends that the firm will pay in the future for as long as it exists. This is the theoretical going concern value of the firm - what it is worth as a functioning business. In general, Market Capitalization is bigger than Equity - if it isn't the firm is worth more as scrap than as an operating business. Um ... no. If you don't have any shares then you are by definition not an owner. Having shares is what makes you an owner. What I think you mean is, is it possible for the owner(s) of a private company to sell all of its shares when it goes public? The answer is yes. It is uncommon for a start-up owner to do this but it is standard practice for "corporate raiders" who buy failing companies, take them private, restructure them and then take them public again - they have done their job and they are not interested in maintaining an ownership stake. Nope. See above and below. Not at all, equity is an accounting construct and market capitalization is about market sentiment. Consider the following hypothetical firm: It has $1m in equity, it makes $4m in profit and will do for the foreseeable future, it pays all of that $4m out as dividends - if we work on a simple ROI of 10% then this firm is worth $40m dollars - way more than its equity.