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Edge bevel is a useful tool for low-poly mesh creation or editing as it allows some latitude with respect to the 'sharpness' of an edge. It's also extremely useful in situations where Mesh Smoothing is used as the additional, and often angled, surfaces facilitate a much better distribution of 'shading' across a mesh.
Simple ('Mesh') Edge Bevel is selection based so the function is only carried out on edges that are actively selected in the 3DView. Edges can be selected as paired vertexes or as edges, and single or multiple selections therein.
Design Note: Simple Edge Bevel is not the same as the Bevel Modifier.
Select the mesh and "Tab" into Edit mode. Use "Ctrl+Tab" to change to either "Edge" or "Vertex" select mode and RMB click an edge or collection of two or more vertexes ("Shift+" to multi-select). With the necessary elements selection from the 3DViews main Header, click "Mesh", "Edges" and then "Bevel" ("Mesh » Edges » Bevel"), the mesh should instantly update to display a sloped surface associated with the previously selected elements, accompanied by a set of ToolShelf options in the left-hand side. To change the depth of the Bevel edit the "Percent:" value but LMB clicking the arrows either side of the input box, LMB+hold+drag the mouse left/right, or click and type a numerical value to change the setting 'up' or 'down' as needed. The slope will update automatically as the value changes. To Bevel additional edges repeat the process.
Design Note: LMB clicking isn't necessary to 'set' the changes, however, if additional edges are selected the ToolShelf option may not disappear, giving the false impression that they can be applied again to the new selection. They cannot so the process has to be redone, which clears the tool options and resets their availability for the next attempt.
Currently, Bevel will produce slightly different results based on what's actually selected. In other words, an edge that terminates at another but unselected edge will produce a different Bevel value that an edge that follows through to another selection. This is due to the way Bevel currently 'averages' values between selected and unselected elements, decreasing the more elements are selected.