Is it possible to set/change a link/image border style?

I do not normally link W3Schools as I do not approve of them as a good source but they do have a full list of border options here:

http://www.w3schools.com/css/css_border.asp

You can also have completly custom borders using CSS3 border-image. CSS3 border-image has very good support in most mordern browsers, unfortunately as normal internet explorer isn't up to par and it is only compatible in IE11 and Edge. Luckily it degrades gracefully by also declaring a normal border.

border-image is probably one of the most complicated new additions to CSS3 and I am not even going to attempt to explain it, but there is an amazing guide over at CSS-tricks with the best explination I have seen:

https://css-tricks.com/understanding-border-image/

You would do this with css which is the style sheet that is used with html. Html is the markup language and css provides the styling.

example css:

a:link, a:visited {
    background-color: white;
    color: black;
    border: 2px solid green;
    padding: 10px 20px;
    text-align: center;
    text-decoration: none;
    display: inline-block;
}

a:hover, a:active {
    background-color: green;
    color: white;
}

What you're doing here is targeting the link with pseudo classes and having it seem like a box with hover effects. In the css above you can replace solid with dotted etc. You can also change the width of the border in pixels etc.

Hopefully this helps. Good Luck.

Taken from W3schools (Values):

dotted - Defines a dotted border
dashed - Defines a dashed border
solid - Defines a solid border
double - Defines a double border
groove - Defines a 3D grooved border. The effect depends on the border-color value
ridge - Defines a 3D ridged border. The effect depends on the border-color value
inset - Defines a 3D inset border. The effect depends on the border-color value
outset - Defines a 3D outset border. The effect depends on the border-color value
none - Defines no border
hidden - Defines a hidden border

Also taken from W3Schools (Properties):

With CSS3, you can give any element "rounded corners", by using the border-radius property. With the CSS3 border-image property, you can set an image to be used as the border around an element.