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A. Kernel Build Example

Here is a kernel build example (in Redhat 9.0). Statements between "/*" and "*/" are in-line comments, not console output.
[root@localhost root]# ln -s /usr/src/linux-2.4.20 /usr/src/linux
[root@localhost root]# cd /usr/src/linux
[root@localhost linux]# make xconfig
        /* Create .config
         *   1. "Load Configuration from File" ->
         *        /boot/config-2.4.20-28.9, or whatever you like
         *   2. Modify kernel configuration parameters
         *   3. "Save and Exit" */
[root@localhost linux]# make oldconfig
        /* Re-check .config, optional */
[root@localhost linux]# vi Makefile
        /* Modify EXTRAVERSION in linux/Makefile, optional */
[root@localhost linux]# make dep
        /* Create .depend and more */
[root@localhost linux]# make bzImage
        /* ... Some output omitted */
ld -m elf_i386 -T /usr/src/linux-2.4.20/arch/i386/vmlinux.lds -e stext arch/i386
/kernel/head.o arch/i386/kernel/init_task.o init/main.o init/version.o init/do_m
ounts.o \
        --start-group \
        arch/i386/kernel/kernel.o arch/i386/mm/mm.o kernel/kernel.o mm/mm.o fs/f
s.o ipc/ipc.o \
         drivers/char/char.o drivers/block/block.o drivers/misc/misc.o drivers/n
et/net.o drivers/media/media.o drivers/char/drm/drm.o drivers/net/fc/fc.o driver
s/net/appletalk/appletalk.o drivers/net/tokenring/tr.o drivers/net/wan/wan.o dri
vers/atm/atm.o drivers/ide/idedriver.o drivers/cdrom/driver.o drivers/pci/driver
.o drivers/net/pcmcia/pcmcia_net.o drivers/net/wireless/wireless_net.o drivers/p
np/pnp.o drivers/video/video.o drivers/net/hamradio/hamradio.o drivers/md/mddev.
o drivers/isdn/vmlinux-obj.o \
        net/network.o \
        /usr/src/linux-2.4.20/arch/i386/lib/lib.a /usr/src/linux-2.4.20/lib/lib.
a /usr/src/linux-2.4.20/arch/i386/lib/lib.a \
        --end-group \
        -o vmlinux
nm vmlinux | grep -v '\(compiled\)\|\(\.o$\)\|\( [aUw] \)\|\(\.\.ng$\)\|\(LASH[R
L]DI\)' | sort > System.map
make[1]: Entering directory `/usr/src/linux-2.4.20/arch/i386/boot'
gcc -E -D__KERNEL__ -I/usr/src/linux-2.4.20/include -D__BIG_KERNEL__ -traditiona
l -DSVGA_MODE=NORMAL_VGA  bootsect.S -o bbootsect.s
as -o bbootsect.o bbootsect.s
bootsect.S: Assembler messages:
bootsect.S:239: Warning: indirect lcall without `*'
ld -m elf_i386 -Ttext 0x0 -s --oformat binary bbootsect.o -o bbootsect
gcc -E -D__KERNEL__ -I/usr/src/linux-2.4.20/include -D__BIG_KERNEL__ -D__ASSEMBL
Y__ -traditional -DSVGA_MODE=NORMAL_VGA  setup.S -o bsetup.s
as -o bsetup.o bsetup.s
setup.S: Assembler messages:
setup.S:230: Warning: indirect lcall without `*'
ld -m elf_i386 -Ttext 0x0 -s --oformat binary -e begtext -o bsetup bsetup.o
make[2]: Entering directory `/usr/src/linux-2.4.20/arch/i386/boot/compressed'
tmppiggy=_tmp_$$piggy; \
rm -f $tmppiggy $tmppiggy.gz $tmppiggy.lnk; \
objcopy -O binary -R .note -R .comment -S /usr/src/linux-2.4.20/vmlinux $tmppigg
y; \
gzip -f -9 < $tmppiggy > $tmppiggy.gz; \
echo "SECTIONS { .data : { input_len = .; LONG(input_data_end - input_data) inpu
t_data = .; *(.data) input_data_end = .; }}" > $tmppiggy.lnk; \
ld -m elf_i386 -r -o piggy.o -b binary $tmppiggy.gz -b elf32-i386 -T $tmppiggy.l
nk; \
rm -f $tmppiggy $tmppiggy.gz $tmppiggy.lnk
gcc -D__ASSEMBLY__ -D__KERNEL__ -I/usr/src/linux-2.4.20/include -traditional -c
head.S
gcc -D__KERNEL__ -I/usr/src/linux-2.4.20/include -Wall -Wstrict-prototypes -Wno-
trigraphs -O2 -fno-strict-aliasing -fno-common -fomit-frame-pointer -pipe -mpref
erred-stack-boundary=2 -march=i686 -DKBUILD_BASENAME=misc -c misc.c
ld -m elf_i386 -Ttext 0x100000 -e startup_32 -o bvmlinux head.o misc.o piggy.o
make[2]: Leaving directory `/usr/src/linux-2.4.20/arch/i386/boot/compressed'
gcc -Wall -Wstrict-prototypes -O2 -fomit-frame-pointer -o tools/build tools/buil
d.c -I/usr/src/linux-2.4.20/include
objcopy -O binary -R .note -R .comment -S compressed/bvmlinux compressed/bvmlinu
x.out
tools/build -b bbootsect bsetup compressed/bvmlinux.out CURRENT > bzImage
Root device is (3, 67)
Boot sector 512 bytes.
Setup is 4780 bytes.
System is 852 kB
make[1]: Leaving directory `/usr/src/linux-2.4.20/arch/i386/boot'
[root@localhost linux]# make modules modules_install
        /* ... Some output omitted */
cd /lib/modules/2.4.20; \
mkdir -p pcmcia; \
find kernel -path '*/pcmcia/*' -name '*.o' | xargs -i -r ln -sf ../{} pcmcia
if [ -r System.map ]; then /sbin/depmod -ae -F System.map  2.4.20; fi
[root@localhost linux]# cp arch/i386/boot/bzImage /boot/vmlinuz-2.4.20
[root@localhost linux]# cp vmlinux /boot/vmlinux-2.4.20
[root@localhost linux]# cp System.map /boot/System.map-2.4.20
[root@localhost linux]# cp .config /boot/config-2.4.20
[root@localhost linux]# mkinitrd /boot/initrd-2.4.20.img 2.4.20
[root@localhost linux]# vi /boot/grub/grub.conf
        /* Add the following lines to grub.conf:
title Linux (2.4.20)
        kernel /vmlinuz-2.4.20 ro root=LABEL=/
        initrd /initrd-2.4.20.img
         */

Refer to Kernelnewbies FAQ: How do I compile a kernel and Kernel Rebuild Procedure for more details.

To build the kernel in Debian, also refer to Debian Installation Manual: Compiling a New Kernel, The Debian GNU/Linux FAQ: Debian and the kernel and Debian Reference: The Linux kernel under Debian. Check "zless /usr/share/doc/kernel-package/Problems.gz" if you encounter problems.