Adding accesspoint-mode to SSRPARI's stretch-branch (found here: https://www.raspberrypi.org/documentation/configuration/wireless/access-point.md)

ap_config.sh

#!/bin/bash
if [ "$WIFIPASS" == "" ]
then
    read -p "Wifi Network name: " APName
    read -p "Wifi Password: " WIFIPASS
fi
if [ -z "$exc" ]
then
    source functions.sh
    source dependencies.sh
fi

sudo systemctl stop dhcpcd
sudo systemctl stop dnsmasq
sudo systemctl stop hostapd

# ======================
# SETUP THE CONFIG FILES
# ======================
#
# STATIC IP / BRIDGE
#
save_original /etc/dhcpcd.conf
    exc patch /etc/dhcpcd.conf <<EOT
@@ -55,3 +55,5 @@
 #interface eth0
 #fallback static_eth0
 
+interface wlan1
+    static ip_address=192.168.1.1/24
EOT

    # Not necessary, but in case someone needs it:
    # BRIDGE
    #
    #save_original /etc/network/interfaces
    #    exc patch /etc/network/interfaces <<EOT
    #@@ -5,3 +5,8 @@
    # 
    # # Include files from /etc/network/interfaces.d:
    # source-directory /etc/network/interfaces.d
    #+
    #+# Bridge setup
    #+auto br0
    #+iface br0 inet manual
    #+bridge_ports eth0 wlan1
    #EOT

sudo service dhcpcd start

#
# ACCES POINT
#
save_original /etc/hostapd/hostapd.conf
    exc patch /etc/hostapd/hostapd.conf <<EOT
@@ -0,0 +1,16 @@
+interface=wlan1
+driver=nl80211
+ssid=$APName
+hw_mode=g
+channel=6
+macaddr_acl=0
+auth_algs=1
+ignore_broadcast_ssid=0
+wpa=2
+wpa_passphrase=$WIFIPASS
+wpa_key_mgmt=WPA-PSK
+#wpa_pairwise=TKIP      # You better do not use this weak encryption (only used by old client devices
+rsn_pairwise=CCMP
+ieee80211n=1
+wmm_enabled=1
+ht_capab=[HT40][SHORT-GI-20][DSSS_CCK-40]
EOT

save_original /etc/default/hostapd
    exc patch /etc/default/hostapd <<EOT
@@ -7,7 +7,7 @@
 # file and hostapd will be started during system boot. An example configuration
 # file can be found at /usr/share/doc/hostapd/examples/hostapd.conf.gz
 #
-#DAEMON_CONF=""
+DAEMON_CONF="/etc/hostapd/hostapd.conf"
 
 # Additional daemon options to be appended to hostapd command:-
 # 	-d   show more debug messages (-dd for even more)
EOT

#
# DHCP-SERVER
#
save_original /etc/dnsmasq.conf
    exc patch /etc/dnsmasq.conf <<EOT
@@ -668,3 +668,6 @@
 # Delays sending DHCPOFFER and proxydhcp replies for at least the specified number of seconds.
 dhcp-mac=set:client_is_a_pi,B8:27:EB:*:*:*
 dhcp-reply-delay=tag:client_is_a_pi,2
+
+interface=wlan1      # Use the require wireless interface - usually wlan0
+  dhcp-range=192.168.1.2,192.168.1.20,255.255.255.0,24h
EOT

#
# ROUTING AND MASQUERADE
#
save_original /etc/sysctl.conf
    exc patch /etc/sysctl.conf <<EOT
@@ -25,7 +25,7 @@
 #net.ipv4.tcp_syncookies=1
 
 # Uncomment the next line to enable packet forwarding for IPv4
-#net.ipv4.ip_forward=1
+net.ipv4.ip_forward=1
 
 # Uncomment the next line to enable packet forwarding for IPv6
 #  Enabling this option disables Stateless Address Autoconfiguration
EOT

sudo iptables -t nat -A  POSTROUTING -o eth0 -j MASQUERADE
sudo sh -c "iptables-save > /etc/iptables.ipv4.nat"

save_original /etc/rc.local
    exc patch /etc/rc.local <<EOT
@@ -17,4 +17,5 @@
   printf "My IP address is %s\n" "$_IP"
 fi
 
+iptables-restore < /etc/iptables.ipv4.nat
 exit 0
EOT

    # Not necessary, but in case someone needs it:
    # BRIDGE
    #
    # sudo brctl addbr br0
    # sudo brctl addif br0 eth0
sudo systemctl start hostapd
sudo systemctl start dnsmasq

My smartphone doen't get an IP when the Pi isn't connected to a LAN-internet-source

bridge-functions not needed
don't forget to add dnsmasq to the dependencies.sh
finished