As mentioned earlier, book value is the value in financial books. There are rules to record it. Book value helps understand the financial working of the company. All liabilities are removed from the assets to get this value. This value is the end for stakeholders. When all assets are sold and liabilities are paid off, we get this value.
When it comes to market value, it is not such a theoretical value. It is a more flexible term. We calculate it by multiplying the current stock price with the number of shares outstanding that we are trading in the market. It is the value at which an asset of the company would trade in the market.