How to detect Safari, Chrome, IE, Firefox and Opera browser?

I have 5 addons/extensions for FF, Chrome, IE, Opera, and Safari.

How can I recognize the user browser and redirect (once an install button has been clicked) to download the corresponding addon?

Googling for browser reliable detection often results in checking the User agent string. This method is not reliable, because it's trivial to spoof this value.
I've written a method to detect browsers by duck-typing.

Only use the browser detection method if it's truly necessary, such as showing browser-specific instructions to install an extension. Use feature detection when possible.

Demo: https://jsfiddle.net/6spj1059/

// Opera 8.0+
var isOpera = (!!window.opr && !!opr.addons) || !!window.opera || navigator.userAgent.indexOf(' OPR/') >= 0;

// Firefox 1.0+
var isFirefox = typeof InstallTrigger !== 'undefined';

// Safari 3.0+ "[object HTMLElementConstructor]" 
var isSafari = /constructor/i.test(window.HTMLElement) || (function (p) { return p.toString() === "[object SafariRemoteNotification]"; })(!window['safari'] || (typeof safari !== 'undefined' && window['safari'].pushNotification));

// Internet Explorer 6-11
var isIE = /*@cc_on!@*/false || !!document.documentMode;

// Edge 20+
var isEdge = !isIE && !!window.StyleMedia;

// Chrome 1 - 79
var isChrome = !!window.chrome && (!!window.chrome.webstore || !!window.chrome.runtime);

// Edge (based on chromium) detection
var isEdgeChromium = isChrome && (navigator.userAgent.indexOf("Edg") != -1);

// Blink engine detection
var isBlink = (isChrome || isOpera) && !!window.CSS;


var output = 'Detecting browsers by ducktyping:<hr>';
output += 'isFirefox: ' + isFirefox + '<br>';
output += 'isChrome: ' + isChrome + '<br>';
output += 'isSafari: ' + isSafari + '<br>';
output += 'isOpera: ' + isOpera + '<br>';
output += 'isIE: ' + isIE + '<br>';
output += 'isEdge: ' + isEdge + '<br>';
output += 'isEdgeChromium: ' + isEdgeChromium + '<br>';
output += 'isBlink: ' + isBlink + '<br>';
document.body.innerHTML = output;

Analysis of reliability

The previous method depended on properties of the rendering engine (-moz-box-sizing and -webkit-transform) to detect the browser. These prefixes will eventually be dropped, so to make detection even more robust, I switched to browser-specific characteristics:

• Internet Explorer: JScript's Conditional compilation (up until IE9) and document.documentMode.
• Edge: In Trident and Edge browsers, Microsoft's implementation exposes the StyleMedia constructor. Excluding Trident leaves us with Edge.
• Edge (based on chromium): The user agent include the value "Edg/[version]" at the end (ex: "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/80.0.3987.16 Safari/537.36 Edg/80.0.361.9").
• Firefox: Firefox's API to install add-ons: InstallTrigger
• Chrome: The global chrome object, containing several properties including a documented chrome.webstore object.
• Update 3 chrome.webstore is deprecated and undefined in recent versions
• Safari: A unique naming pattern in its naming of constructors. This is the least durable method of all listed properties and guess what? In Safari 9.1.3 it was fixed. So we are checking against SafariRemoteNotification, which was introduced after version 7.1, to cover all Safaris from 3.0 and upwards.
• Opera: window.opera has existed for years, but will be dropped when Opera replaces its engine with Blink + V8 (used by Chromium).
• Update 1: Opera 15 has been released, its UA string looks like Chrome, but with the addition of "OPR". In this version the chrome object is defined (but chrome.webstore isn't). Since Opera tries hard to clone Chrome, I use user agent sniffing for this purpose.
• Update 2: !!window.opr && opr.addons can be used to detect Opera 20+ (evergreen).
• Blink: CSS.supports() was introduced in Blink once Google switched on Chrome 28. It's of course, the same Blink used in Opera.

Successfully tested in:

• Firefox 0.8 - 61
• Chrome 1.0 - 71
• Opera 8.0 - 34
• Safari 3.0 - 10
• IE 6 - 11
• Edge - 20-42
• Edge Dev - 80.0.361.9

Updated in November 2016 to include detection of Safari browsers from 9.1.3 and upwards

Updated in August 2018 to update the latest successful tests on chrome, firefox IE and edge.

Updated in January 2019 to fix chrome detection (because of the window.chrome.webstore deprecation) and include the latest successful tests on chrome.

Updated in December 2019 to add Edge based on Chromium detection (based on the @Nimesh comment).

You can try following way to check Browser version.

    <!DOCTYPE html>
    <html>
    <body>
    <p>What is the name(s) of your browser?</p>
    <button onclick="myFunction()">Try it</button>
    <p id="demo"></p>
    <script>
    
    function myFunction() { 
     if((navigator.userAgent.indexOf("Opera") || navigator.userAgent.indexOf('OPR')) != -1 ) 
    {
        alert('Opera');
    }
    else if(navigator.userAgent.indexOf("Edg") != -1 )
    {
        alert('Edge');
    }
    else if(navigator.userAgent.indexOf("Chrome") != -1 )
    {
        alert('Chrome');
    }
    else if(navigator.userAgent.indexOf("Safari") != -1)
    {
        alert('Safari');
    }
    else if(navigator.userAgent.indexOf("Firefox") != -1 ) 
    {
         alert('Firefox');
    }
    else if((navigator.userAgent.indexOf("MSIE") != -1 ) || (!!document.documentMode == true )) //IF IE > 10
    {
      alert('IE'); 
    }  
    else 
    {
       alert('unknown');
    }
    }
    </script>
    
    </body>
    </html>

And if you need to know only IE Browser version then you can follow below code. This code works well for version IE6 to IE11

<!DOCTYPE html>
<html>
<body>

<p>Click on Try button to check IE Browser version.</p>

<button onclick="getInternetExplorerVersion()">Try it</button>

<p id="demo"></p>

<script>
function getInternetExplorerVersion() {
   var ua = window.navigator.userAgent;
        var msie = ua.indexOf("MSIE ");
        var rv = -1;

        if (msie > 0 || !!navigator.userAgent.match(/Trident.*rv\:11\./))      // If Internet Explorer, return version number
        {               

            if (isNaN(parseInt(ua.substring(msie + 5, ua.indexOf(".", msie))))) {
                //For IE 11 >
                if (navigator.appName == 'Netscape') {
                    var ua = navigator.userAgent;
                    var re = new RegExp("Trident/.*rv:([0-9]{1,}[\.0-9]{0,})");
                    if (re.exec(ua) != null) {
                        rv = parseFloat(RegExp.$1);
                        alert(rv);
                    }
                }
                else {
                    alert('otherbrowser');
                }
            }
            else {
                //For < IE11
                alert(parseInt(ua.substring(msie + 5, ua.indexOf(".", msie))));
            }
            return false;
        }}
</script>

</body>
</html>