When working in .NET you pretty much have to re-learn the VCL, (FCL) to accomplish every single task

there's tons of code for Win32 to convert images to/from formats, here I show  you how to convert an Image from BMP to any format (JPG, PNG, GIF, etc) in .NET

the FCL provides methods to do many image manipulation tricks, you just have to know where to find them

this function will do the job for you

procedure TWinForm3.Bmp2AnyFormat(theBmp:Bitmap; const FileName:string; const ImgFormat:ImageFormat);
var
  fs:FileStream;
begin
  fs:=FileStream.Create(FileName, FileMode.CreateNew);
  try try
    theBmp.Save(fs, ImgFormat);
  except
    on E:Exception do
      raise Exception.Create('Error converting image: '+E.Message);
  end finally
    fs.Close
  end
end;

the Bitmap class comes from
System.Drawing.Imaging

the FileStream comes from:
System.IO

so you'll need those in your uses clause

now, an example of use:
say you have a PictureBox with a .BMP on it in your form, and you wanted to save that as a jpeg

I put some code to load a bmp at runtime:
procedure TWinForm3.TWinForm3_Load(sender: System.Object; e: System.EventArgs);
begin
  PictureBox1.Image:=Image.FromFile('c:\SomeFile.bmp');
end;

then a button to convert the image (to JPEG) using the function:
procedure TWinForm3.Button1_Click(sender: System.Object; e: System.EventArgs);
begin
  Bmp2AnyFormat(Bitmap(PictureBox1.Image), 'f:\new.jpg', ImageFormat.Jpeg)
end;

you can use
ImageFormat.Tiff,
ImageFormat.Gif,
ImageFormat.Png,
ImageFormat.Jpeg,
etc...

that's it, as you can see, is really easy... the hard part is to find which class does what

best regards