Simple browser detection via user agent string for Chrome/IE/Firefox/Opera/Safari. For if you absolutely _have_ to browser detect rather than feature detect...

browserDetect.js

/**
 * @name browserDetect
 * @description
 * Parses the User Agent string to determine browser and version information, as applicable. Reliably detects major
 * versions of the following:
 * * Chrome
 * * Internet Explorer
 * * Edge
 * * Safari
 * * Firefox
 * * Opera
 *
 * @returns {{major: number, minor: number, patch: number, build: number, browser: string}}
 */
function browserDetect() {
    'use strict';

    var UA = ( navigator || window.navigator ).userAgent.toLowerCase(),
        tests = {
            // no minor or patch, but at least we get a build?
            edge:    /edge\/(\d+)\.(\d+)/,
            // mostly only reports major version with unnecessary ".0" suffix
            firefox: /firefox\/(\d+(?:\.\d+)*)/,
            // sure, there are other tests, but they're complicated and unreliable
            ie:      /trident\/(\d+)/,
            // ie <=7, unsupported by any sane creature
            oldIE:   /msie\/(\d+)/,
            // has to be checked for, lest it be mistaken for Safari or Chrome
            opera:   /opr\/(\d+(?:\.\d+)*)/,
            // both of these have to be present; other browsers like to pretend to be Safari
            safari:  [
                /safari\/(\d+(?:\.\d+)*)/, // build
                /version\/(\d+(?:\.\d+)*)/ // major/minor/patch
            ],
            // Note: chrome test is only true if all other tests are false; practically everyone pretends to be Chrome
            chrome:  /chrome\/(\d+(?:\.\d+)*)/
        },
        // what we'll be exposing
        details = {
            major:   0,
            minor:   0,
            patch:   0,
            build:   0,
            browser: ''
        };

    /**
     * @name splitFour
     * @description
     * Takes the result of a `String.match` call, splits the returned inner match on decimals, and assigns the resulting
     * version number parts to the details object
     * @private
     * 
     * @param {Array} match  Result of a `String.match` call. Should have an inner match at index 1
     */
    function splitFour( match ) {

        var versions = match[1].split( '.' );

        details.major = versions[0];
        if( versions[1] ) details.minor = versions[1];
        if( versions[2] ) details.patch = versions[2];
        if( versions[3] ) details.build = versions[3];

    }

    // Edge
    if( tests.edge.test( UA ) ) {

        details.browser = 'Edge';
        // Edge exposes a major version number, but sadly the only _other_ thing it exposes is the Windows Build number.
        details.major = UA.match( tests.edge )[1];
        details.build = UA.match( tests.edge )[2];

        // IE 8-11
    } else if( tests.ie.test( UA ) ) {

        details.browser = 'IE';
        // IE doesn't tell you _squat_ about versioning beyond the major number, which it doesn't necessarily tell you straight, either
        switch( UA.match( tests.ie )[1] ) {
            case '7':
                details.major = 11;
                break;
            case '6':
                details.major = 10;
                break;
            case '5':
                details.major = 9;
                break;
            case '4':
                details.major = 8;
                break;
        }

    // IE <8
    } else if( tests.oldIE.test( UA ) ) {

        // we're dealing with ancient artifacts here, Indy
        details.browser = 'IE';
        details.major = UA.match( tests.oldIE )[1];

    // Firefox
    } else if( tests.firefox.test( UA ) ) {

        details.browser = 'Firefox';
        splitFour( UA.match( tests.firefox ) );

    // Opera
    } else if( tests.opera.test( UA ) ) {

        details.browser = 'Opera';
        splitFour( UA.match( tests.opera ) );

    // Safari
    } else if( tests.safari[0].test( UA ) && tests.safari[1].test( UA ) ) {

        details.browser = 'Safari';
        // safari reports its major/minor/patch versions directly under Version/a.b.c
        splitFour( UA.match( tests.safari[1] ) );
        // build is reported separately, under the Safari/x.y.z format
        details.build = UA.match( tests.safari[0] )[1];

    // Chrome
    } else if( tests.chrome.test( UA ) ) {

        details.browser = 'Chrome';
        splitFour( UA.match( tests.chrome ) );

    // Browser Incognita
    } else {
        // do we care at this point?
        details.browser = '?';
    }

    return details;

}