With Low Search, you do not "form a URL", but rather you create a search form that you can submit, which will generate the URL for you. How you create the elements in your form depends on what types of filters you will need and how you set up your channels and fields.
For the alphabet, you can use the Field Search filter, but you'd have to hard-code the options yourself. Here I'm targetting the title
, but you can target a custom field, too.
<select name="search:title[]" multiple>
<option value="a">A</option>
<option value="b">B</option>
...
</select>
<input type="hidden" name="starts_with" value="search:title">
For the style, if that is a custom field, also use the Field Search filter:
<select name="search:my_style_field[]" multiple>
<option value="Style 1">Style 1</option>
<option value="Style 2">Style 2</option>
...
</select>
<input type="hidden" name="exact" value="search:my_style_field">
For the country, if that is a category group, use the Categories filter:
<select name="category[]" multiple>
{exp:channel:categories style="linear"}
<option value="{category_id}">{category_name}</option>
{/exp:channel:categories}
</select>
<input type="hidden" name="require_all" value="category">
And put all that inside the Form.
Be sure to read all the docs on Parameters, Filters, and Template Tags before checking out the example page.