I didn't find "ZipFile" class in the "System.IO.Compression" namespace

You need an extra reference for this; the most convenient way to do this is via the NuGet package System.IO.Compression.ZipFile

<!-- Version here correct at time of writing, but please check for latest -->
<PackageReference Include="System.IO.Compression.ZipFile" Version="4.3.0" />

If you are working on .NET Framework without NuGet, you need to add a dll reference to the assembly, "System.IO.Compression.FileSystem.dll" - and ensure you are using at least .NET 4.5 (since it doesn't exist in earlier frameworks).

For info, you can find the assembly and .NET version(s) from MSDN

For those who are green programmers in .NET, to add the DLL reference as MarcGravell noted, you follow these steps:

To add a reference in Visual C#

1. In Solution Explorer, right-click the project node and click Add Reference.
2. In the Add Reference dialog box, select the tab indicating the type of component you want to reference.
3. Select the components you want to reference, and then click OK.

From the MSDN Article, How to: Add or Remove References By Using the Add Reference Dialog Box.

you can use an external package if you cant upgrade to 4.5. One such is Ionic.Zip.dll from DotNetZipLib.

using Ionic.Zip;

you can download it here, its free. http://dotnetzip.codeplex.com/