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Add custom fonts to the "Typography" section of the Salient Theme Options Panel Option #1: Use a plugin

The plugin Use Any Font will allow you to upload custom fonts via a user interface and automatically add them into the Salient options panel > Typography tab as options. This approach is the easiest approach.

Option #2: Add font programmatically

If you would rather add new fonts via custom WordPress filters/font-face rules, there are several options.

•  http://www.wpbeginner.com/wp-themes/how-add-google-web-fonts-wordpress-themes/ 
• http://www.wpbeginner.com/plugins/how-to-add-awesome-typography-in-wordpress-with-typekit/ . 
• @font-face https://premium.wpmudev.org/blog/custom-fonts-css/

- The Below example uses the @font-face method and the fonts are included in a Child Theme.

Step 1:

@font-face CSS methods are included in the Salient Theme Options Panel -> General Settings -> Custom CSS Box to import the relevant font files.

@font-face {
    font-family: 'Proxima Nova Light';
    src: url("/wp-content/themes/salient-child/fonts/ProximaNova-Light.woff") format("woff"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-Light.otf") format("opentype"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-Light.ttf") format("truetype");
    font-weight: 300;
    font-style: normal;
}
@font-face {
    font-family: 'Proxima Nova LightIt';
    src: url("/wp-content/themes/salient-child/fonts/ProximaNova-LightIt.woff") format("woff"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-LightIt.otf") format("opentype"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-LightIt.ttf") format("truetype");
    font-weight: 300;
    font-style: italic;
}
@font-face {
    font-family: 'Proxima Nova Regular';
    src: url("/wp-content/themes/salient-child/fonts/ProximaNova-Regular.woff") format("woff"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-Regular.otf") format("opentype"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-Regular.ttf") format("truetype");
    font-weight: normal;
    font-style: normal;
}
@font-face {
    font-family: 'Proxima Nova RegularIt';
    src: url("/wp-content/themes/salient-child/fonts/ProximaNova-RegularIt.woff") format("woff"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-RegularIt.otf") format("opentype"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-RegularIt.ttf") format("truetype");
    font-weight: normal;
    font-style: italic;
}
@font-face {
    font-family: 'Proxima Nova Semibold';
    src: url("/wp-content/themes/salient-child/fonts/ProximaNova-Semibold.woff") format("woff"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-Semibold.otf") format("opentype"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-Semibold.ttf") format("truetype");
    font-weight: 600;
    font-style: normal;
}
@font-face {
    font-family: 'Proxima Nova SemiboldIt';
    src: url("/wp-content/themes/salient-child/fonts/ProximaNova-SemiboldIt.woff") format("woff"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-SemiboldIt.otf") format("opentype"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-SemiboldIt.ttf") format("truetype");
    font-weight: 600;
    font-style: italic;
}
@font-face {
    font-family: 'Proxima Nova Bold';
    src: url("/wp-content/themes/salient-child/fonts/ProximaNova-Bold.woff") format("woff"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-Bold.otf") format("opentype"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-Bold.ttf") format("truetype");
    font-weight: bold;
    font-style: normal;
}
@font-face {
    font-family: 'Proxima Nova BoldIt';
    src: url("/wp-content/themes/salient-child/fonts/ProximaNova-BoldIt.woff") format("woff"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-BoldIt.otf") format("opentype"),
        url("/wp-content/themes/salient-child/fonts/ProximaNova-BoldIt.ttf") format("truetype");
    font-weight: bold;
    font-style: italic;
}

Step 2: 

Add PHP Code using Code Snippets Plugin for the Salient Theme Options -> Typography Section Fields.

function salient_redux_custom_fonts() {
    return array(
        'Custom Fonts' => array(
            'Proxima Nova Light' => 'Proxima Nova Light',
            'Proxima Nova LightIt' => 'Proxima Nova LightIt',
            'Proxima Nova Regular' => 'Proxima Nova Regular',
            'Proxima Nova RegularIt' => 'Proxima Nova RegularIt',
            'Proxima Nova Semibold' => 'Proxima Nova Semibold',
            'Proxima Nova SemiboldIt' => 'Proxima Nova SemiboldIt',
            'Proxima Nova Bold' => 'Proxima Nova Bold',
            'Proxima Nova BoldIt' => 'Proxima Nova BoldIt'
        )
    );
}
add_filter( "redux/salient_redux/field/typography/custom_fonts", "salient_redux_custom_fonts" );

Conclusion: 

You should be able to now select the Custom Fonts from the Typography Section in the Salient Theme Options.

Adds Salient compatibility to https://wordpress.org/plugins/custom-typekit-fonts/ plugin

Add PHP Code using Code Snippets Plugin 

// Adds Salient compatibility to https://wordpress.org/plugins/custom-typekit-fonts/ plugin 
function salient_redux_typekit_fonts() {
    
    $kit_info = get_option( 'custom-typekit-fonts' );
    if (!empty($kit_info)):
        foreach ($kit_info['custom-typekit-font-details'] as $fontArr):
            $fontCssName=$fontArr['css_names'][0];
            $fonts_typekit['Typekit Fonts'][$fontCssName]= $fontCssName;
        endforeach;
    endif;
      return $fonts_typekit;
}
add_filter( "redux/salient_redux/field/typography/custom_fonts", "salient_redux_typekit_fonts" );

Best,