Array formulas in Microsoft Excel are unique types of formulas that operate on a range of values, or an array, rather than individual data points. They enhance the capabilities of Excel by enabling more complex calculations and manipulations of your data. Firstly, the term 'array' simply refers to a range or series of data in rows and columns. For instance, in Excel, an array can be a single column of data, a single row of data, or even a block of cells of data. Let's dive deeper to understand array formulas and their usage: **Using an array formula:** Unlike a regular formula, an array formula is entered by pressing `Ctrl+Shift+Enter` in Windows or `Command+Shift+Enter` on a Mac. When you do this, Excel wraps the formula in curly braces `{ }`. These curly braces indicate that this is an array formula. Please note, you should not manually type these braces. **Performing calculations:** One major use of array formulas lies in performing mathematical operations (like sum, count, average) on two or more ranges of data. For example, if you want to find the sum of the product of two series of numbers, you could use an array formula like `=SUM(A1:A3*B1:B3)` **Handling complex data manipulations:** Excel array formulas are also especially useful when dealing with complex data manipulations, like swapping columns, transforming a horizontal block of cells to vertical (or vice-versa), or even multiplying a range of values by another range of values. **Dealing with text strings:** With array formulas, Excel can handle operations on text strings in ways not possible with standard formulas. This could include getting a unique list of names from a larger list, counting the occurrence of a certain word, or even extracting specific parts of a string across an array. **Conditional Operations:** This is another strong area of array formulas where you can perform operation like sum, count, average etc. on an array based on certain criteria. For example, to sum values in `B1:B5` where corresponding values in `A1:A5` are more than 10, you could use `=SUM(IF(A1:A5>10,B1:B5))`. Remember, array formulas can perform powerful calculations not possible with standard Excel formulas, but they can also be more complex and harder to understand. It is also worth noting that array formulas can slow down a large workbook because of the processing power they require. Hence, use them strategically and when you have a specific need that is best solved with this powerful tool. Lastly, Microsoft Excel has transitioned some functionality of array formulas to dynamic arrays with the introduction of Excel 365. Dynamic arrays are more efficient and easier to use, so if your version of Excel supports it, you may want to explore those as well.